lesson 2 problem solving practice reflections answer key

888-309-8227
732-384-0146

New User Registration

Forgot Password

Textbook Resources

Textbook resources.

Call us toll-free
FAQs – Frequently Asked Questions
Contact Lumos Learning – Proven Study Programs by Expert Teachers

Follow us: Lumos Learning -->

2024 © Lumos Learning
Privacy Policy - Terms of Service - Disclaimers

PARCC® is a registered trademark of PARCC, Inc. Lumos Learning, is not owned by or affiliated in any fashion with PARCC, Inc... Read More

PARCC® is a registered trademark of PARCC, Inc. Lumos Learning, is not owned by or affiliated in any fashion with PARCC, Inc., the Partnership for the Assessment of Readiness for College and Careers, nor any state of the Union. Neither PARCC, Inc., nor The Partnership for the Assessment of Readiness for College and Careers, nor any member state has endorsed this product. No portion of any fees or charges paid for any products or services Lumos Learning offers will be paid or inure to the benefit of PARCC, Inc., or any state of the Union

SBAC is a copyright of The Regents of the University of California – Smarter Balanced Assessment Consortium, which is not aff... Read More

SBAC is a copyright of The Regents of the University of California – Smarter Balanced Assessment Consortium, which is not affiliated to Lumos Learning. The Regents of the University of California – Smarter Balanced Assessment Consortium, was not involved in the production of, and does not endorse these products or this site.

ACT® Aspire™ is a registered trademark of ACT Aspire LLC., which is not affiliated to Lumos Learning. ACT Aspire LLC, was not... Read More

ACT® Aspire™ is a registered trademark of ACT Aspire LLC., which is not affiliated to Lumos Learning. ACT Aspire LLC,was not involved in the production of, and does not endorse these products or this site.

Florida Department of Education is not affiliated to Lumos Learning. Florida department of education, was not involved in the... Read More

Florida Department of Education is not affiliated to Lumos Learning. Florida department of education, was not involved in the production of, and does not endorse these products or this site.

Indiana Department of Education is not affiliated to Lumos Learning. Indiana department of education, was not involved in the... Read More

Indiana Department of Education is not affiliated to Lumos Learning. Indiana department of education, was not involved in the production of, and does not endorse these products or this site.

Mississippi Department of Education is not affiliated to Lumos Learning. Mississippi department of education, was not involved... Read More

Mississippi Department of Education is not affiliated to Lumos Learning. Mississippi department of education, was not involved in the production of, and does not endorse these products or this site.

Ohio Department of Education is not affiliated to Lumos Learning. Ohio department of education, was not involved in the prod... Read More

Ohio Department of Education is not affiliated to Lumos Learning. Ohio department of education, was not involved in the production of, and does not endorse these products or this site.

Tennessee Department of Education is not affiliated to Lumos Learning. Tennessee department of education, was not involved... Read More

Tennessee Department of Education is not affiliated to Lumos Learning. Tennessee department of education, was not involved in the production of, and does not endorse these products or this site.

Georgia Department of Education is not affiliated to Lumos Learning. Georgia department of education, was not involved... Read More

Georgia Department of Education is not affiliated to Lumos Learning. Georgia department of education, was not involved in the production of, and does not endorse these products or this site.

Missouri Department of Education is not affiliated to Lumos Learning. Missouri department of education, was not involved... Read More

Missouri Department of Education is not affiliated to Lumos Learning. Missouri department of education, was not involved in the production of, and does not endorse these products or this site.

Louisiana Department of Education is not affiliated to Lumos Learning. Louisiana department of education, was not involved... Read More

Louisiana Department of Education is not affiliated to Lumos Learning. Louisiana department of education, was not involved in the production of, and does not endorse these products or this site.

Texas Go Math
Big Ideas Math
Engageny Math
McGraw Hill My Math
enVision Math
180 Days of Math
Math in Focus Answer Key
Math Expressions Answer Key
Privacy Policy

$CCSS Math Answers$

Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence

There are multiple ways to learn maths. But choosing the best material is also important for the students to score good marks and also to improve their knowledge. This will be possible only with the help of our Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence. You can get the explanation for all the questions in detail in Go Math Grade 8 Chapter 9 Transformations and Congruence Answer Key here. Refer to Go Math Grade 8 Answer Key for learning the problems in an easy manner.

Practice makes you perfect become a master in maths. Without proper knowledge on the subject, you cannot solve the problems in real-time. This will affect your exam. So, keeping this in our mind we have prepared the solutions briefly which will help you to understand the concept in depth. Get free access to Download Go Math Grade 8 Chapter 9 Transformations and Congruence Solution Key pdf. In this article, you will get the solutions according to the topics. Therefore, students who want to score good marks in the exam must practice with Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence.

Lesson 1: Properties of Translations

Properties of Translations – Page No. 282
Properties of Translations – Page No. 283
Properties of Translations Lesson Check – Page No. 284

Lesson 2: Properties of Reflections

Properties of Reflections – Page No. 288
Properties of Reflections – Page No. 289
Properties of Reflections Lesson Check – Page No. 290
Properties of Reflections Lesson Check 1 – Page No. 294
Properties of Reflections Lesson Check 2 – Page No. 295
Properties of Reflections Lesson Check 3 – Page No. 296

Lesson 3: Algebraic Representations of Transformations

Algebraic Representations of Transformations – Page No. 300
Algebraic Representations of Transformations – Page No. 301
Algebraic Representations of Transformations Lesson Check – Page No. 302

Lesson 4: Congruent Figures

Congruent Figures – Page No. 306
Congruent Figures – Page No. 307
Congruent Figures Lesson Check – Page No. 308
Model Quiz – Page No. 309

Mixed Review

Mixed Review – Page No. 310

Guided Practice – Properties of Translations – Page No. 282

Question 1. Vocabulary A __________________is a change in the position, size, or shape of a figure. ____________

Answer: transformation

Explanation: A transformation is a change in the position, size, or shape of a figure.

Question 2. Vocabulary When you perform a transformation of a figure on the coordinate plane, the input of the transformation is called the ________________, and the output of the transformation is called the_________________ . Type below: ____________

Answer: pre-image image

Explanation: When you perform a transformation of a figure on the coordinate plane, the input of the transformation is called the pre-image, and the output of the transformation is called the image.

Question 3. Joni translates a right triangle 2 units down and 4 units to the right. How does the orientation of the image of the triangle compare with the orientation of the preimage? Orientation is: _______

Answer: Orientation is: Same

Explanation: Since translation does not change the shape and size of a geometric figure, the two triangles are identical in shape and size, so they are congruent and the orientation is the same

Question 4. Rashid drew rectangle PQRS on a coordinate plane. He then translated the rectangle 3 units up and 3 units to the left and labeled the image P ‘Q ‘R ‘S ‘. How do rectangle PQRS and rectangle P ‘Q ‘R ‘S ‘ compare? They are: _______

Answer: congruent

Explanation: Since translation does not change the shape and size of a geometric figure, the two rectangles are identical in shape and size, so they are congruent.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 1$

Answer: After translation: W'(-4, 3) X'(2, 3) Y'(1, 1) Z'(-3, 1)

ESSENTIAL QUESTION CHECK-IN

Question 6. What are the properties of translations? Type below: ____________

Answer: -> a translation is a geometric transformation that moves every point of a figure or space by the same amount in a given direction. -> So the figures are identical and are congruent.

9.1 Independent Practice – Properties of Translations – Page No. 283

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 2$

Answer: 2 left, and 4 down

Question 7. b. How would you describe the translation? Type below: ____________

Answer: It has the same size, shape. and orientation, but a different location

Question 7. c. How does the image of triangle DEF compare with the preimage? ____________

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 3$

Question 8. b. On the same coordinate grid, graph the image of quadrilateral KLMN after a translation of 3 units to the right and 4 units up. Type below: ____________

Question 8. c. Which side of the image is congruent to side $\overline { LM } $? ___________ Name three other pairs of congruent sides. ___________ Type below: ____________

Answer: Line LM is congruent to Line L!M! Line KL is equal to K’L’ Line MN is equal to M’N’ Line KN is equal to K’N’

Draw the image of the figure after each translation.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 4$

Answer: After translation P'(-3, 1) Q'(0, 2) R'(0, -1) S'(-3, -3)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 5$

Answer: After translation A'(0, 4) B'(3, 5) C'(3, 1) D'(0, 0)

Properties of Translations – Page No. 284

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 6$

Answer: 4 units along positive X and 5 units along positive Y

Explanation: Initial coordinate of balloon = ( -2 , -4) Final coordinates of the balloon = (2,1) Translation along x axis = 2 – (-2) = 4 units along positive x direction Translation along y axis = 1-(-4) = 5 units along the positive y direction

Question 12. Critical Thinking Is it possible that the orientation of a figure could change after it is translated? Explain. _________

Answer: No, it is not possible to change the orientation just by translation. As translation means, a transformation in which a figure is moved to another location without any change in size or orientation.

FOCUS ON HIGHER ORDER THINKING

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 7$

Question 13. b. On the same coordinate grid, graph and label triangle X’Y’Z’, the image of triangle XYZ after a translation of 3 units to the left and 6 units up.

Question 13. c. Now graph and label triangle X”Y”Z”, the image of triangle X’Y’Z’ after a translation of 1 unit to the left and 2 units down. Type below: ____________

Question 13. d. Analyze Relationships How would you describe the translation that maps triangle XYZ onto triangle X”Y”Z”? Type below: ____________

Answer: Triangle XYZ has translated 4 units up and 4 units to the left

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 8$

Question 15. Communicate Mathematical Ideas Explain why the image of a figure after a translation is congruent to its preimage. Type below: ____________

Answer: A translation is a geometric transformation that moves every point of a figure or space by the same amount in a given direction. So the 2 figures are identical and the translated figure is congruent to its pre-image.

Guided Practice – Properties of Reflections – Page No. 288

Question 1. Vocabulary A reflection is a transformation that flips a figure across a line called the __________ . ____________

Answer: Reflection Axis

Explanation: A reflection is a transformation that flips a figure across a line called the Reflection Axis.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 2: Properties of Reflections img 9$

Answer: A'(-3, -4) B'(1, -4) C'(3, -1) D'(-3, -1)

Question 2. b. How do trapezoid ABCD and trapezoid A’B’C’D’ compare? ____________

Explanation: trapezoid ABCD and trapezoid A’B’C’D’ are congruent

Question 2. c. What If? Suppose you reflected trapezoid ABCD across the y-axis. How would the orientation of the image of the trapezoid compare with the orientation of the preimage? Type below: ____________

Answer: The orientation would be reversed horizontally.

Question 3. What are the properties of reflections? Type below: ____________

Answer: properties of reflections -> the size stays the same -> the shape stays the same -> the orientation does NOT stay the same

9.2 Independent Practice – Properties of Reflections – Page No. 289

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 2: Properties of Reflections img 10$

Question 4. Which two triangles are reflections of each other across the x-axis? Type below: ____________

Answer: Triangles A and C are the reflections of each other across the x-axis.

Question 5. For which two triangles is the line of reflection the y-axis? Type below: ____________

Answer: For triangle C & D the line of reflection is y-axis.

Question 6. Which triangle is a translation of triangle C? How would you describe the translation? Type below: ____________

Answer: Triangle B is the translation of triangle C. Lets take any one point of the triangle = (-2, -6) Lets take the corresponding side of triangle B = (4,2) Translation across x axis = 4 -(-2) = 6 units Translation across y axis = 2 -(-6) = 8 units

Question 7. Which triangles are congruent? How do you know? Type below: ____________

Answer: All the 4 triangles A, B, C, D are congruent. The length of base and height of all the four triangles are 3 units, 4 units respectively.

Explanation: All the 4 triangles A, B, C, D are congruent. If base and height are equal then the hypotenuse should also be equal. Thus all three sides of the triangles A,B,C,D are equal. Thus these triangles are congruent, The length of base and height of all the four triangles are 3 units, 4 units respectively.

Question 8. a. Graph quadrilateral WXYZ with vertices W(-2, -2), X(3, 1), Y(5, -1), and Z(4, -6) on the coordinate grid. Type below: ____________

Question 8. b. On the same coordinate grid, graph quadrilateral W’X’Y’Z’, the image of quadrilateral WXYZ after a reflection across the x-axis. Type below: ____________

Question 8. c. Which side of the image is congruent to side $\overline { YZ } $? _______________ Name three other pairs of congruent sides. _______________ Type below: ____________

Answer: Line YZ = Line Y’Z’ Line WX = Line W’X’ Line XY = Line X’Y’ Line WZ = Line W’Z’

Question 8. d. Which angle of the image is congruent to ∠X? _______________ Name three other pairs of congruent angles. _______________ Type below: ____________

Answer: Angle X’ Angle W and Angle W’ Angle Y and Angle Y’ Angle Z and Angle Z’

Properties of Reflections – Page No. 290

Question 9. Critical Thinking Is it possible that the image of a point after a reflection could be the same point as the preimage? Explain. ________

Answer: Yes

Explanation: It is possible that the image of a point after a reflection could be the same point as the preimage

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 2: Properties of Reflections img 11$

Question 10. b. On the same coordinate grid, graph the image of the figure you drew in part a after a reflection across the x-axis. Type below: ____________

Question 10. c. Make a Conjecture What other sequence of transformations would produce the same final image from the original preimage? Check your answer by performing the transformations. Then make a conjecture that generalizes your findings. Type below: ____________

Answer: The same image can be obtained by reflecting first across the x-axis and then across the y-axis. Reflecting a figure first across the y-axis and then across the x-axis has the same outcome,. reflecting first across the x-axis and then across the y-axis.

Question 11. a. Graph triangle DEF with vertices D(2, 6), E(5, 6), and F(5, 1) on the coordinate grid.

Question 11. b. Next graph triangle D ′E ′F ′, the image of triangle DEF after a reflection across the y-axis. Type below: ____________

Question 11. c. On the same coordinate grid, graph triangle D′′ E′′ F′′, the image of triangle D ′E ′F ′ after a translation of 7 units down and 2 units to the right. Type below: ____________

Question 11. d. Analyze Relationships Find a different sequence of transformations that will transform triangle DEF to triangle D ′′E ′′F ′′. Type below: ____________

Answer: Translate triangle DEF 7 units down and 2 units to the left. Then reflect the image across the y-axis.

Guided Practice – Properties of Reflections – Page No. 294

Question 1. Vocabulary A rotation is a transformation that turns a figure around a given _____ called the center of rotation. ____________

Answer: point

Explanation: A rotation is a transformation that turns a figure around a given point called the center of rotation.

Siobhan rotates a right triangle 90° counterclockwise about the origin.

Question 2. How does the orientation of the image of the triangle compare with the orientation of the preimage? Type below: ____________

Answer: Each leg in the preimage is perpendicular to its corresponding leg in the image.

Question 3. Is the image of the triangle congruent to the preimage? ______

Explanation: The image of the triangle is congruent to the preimage

Draw the image of the figure after the given rotation about the origin.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 12$

Answer: After 180° rotation A'(-2, -3) B'(-4, -1) C'(-2, 0) D'(0, -1)

Question 6. What are the properties of rotations? Type below: ____________

Answer: Rotations preserve size and shape but change orientation.

9.3 Independent Practice – Properties of Reflections – Page No. 295

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 14$

Answer: ABC was rotated 90º counterclockwise about the origin

Question 7. b. What are the coordinates of the image? Type below: ____________

Answer: A'(3, 1) B'(2, 3) C'(-1, 4)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 15$

Answer: The figure was rotated 180º about the origin.

Question 8. b. Can you describe this as a transformation other than a rotation? Explain. ____________

Explanation: This can also be described as a reflection across the y-axis.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 16$

Answer: A 180º rotation about the origin will preserve the orientation of the H-shaped figure in the grid.

Question 10. A point with coordinates (-2, -3) is rotated 90° clockwise about the origin. What are the coordinates of its image? (_______ , _______)

Answer: (-3, 2)

Explanation: The new coordinates are (-3, 2)

Complete the table with rotations of 180° or 90°. Include the direction of rotation for rotations of 90°.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 17$

Properties of Reflections – Page No. 296

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 18$

Answer: After 180° A'(4, 0) B'(2, -1) C'(0, 0) D'(2, 1)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 19$

Answer: After 270º counterclockwise rotation A'(1, 2) B'(2, -1) C'(4, 2)

Question 16. Is there a rotation for which the orientation of the image is always the same as that of the preimage? If so, what? ______

Explanation: A 360º rotation will always be the same as the original image

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 20$

Answer: Figure A: 2 time(s) Figure B: 1 time(s) Figure C: 4 time(s)

Explanation: 2 times to return to original orientation 1 time to return to original orientation 4 times to return to original orientation

Question 18. Make a Conjecture Triangle ABC is reflected across the y-axis to form the image A′B′C′. Triangle A′B′C′ is then reflected across the x-axis to form the image A″B″C″. What type of rotation can be used to describe the relationship between triangle A″B″C″ and triangle ABC? Type below: ____________

Answer: Triangle A’B’C’ is a 90º rotation of triangle ABC Triangle A”B”C” is a 90º rotation of triangle A’B’C’ Therefore, Triangle A”B”C” is a 180º rotation of triangle ABC

Question 19. Communicate Mathematical Ideas Point A is on the y-axis. Describe all possible locations of image A′ for rotations of 90°, 180°, and 270°. Include the origin as a possible location for A. Type below: ____________

Answer: If Point A is on the y-axis, Point A’ will be on the x-axis for 190° and 270° rotations and on the y-axis for 180° rotation If point A is at the origin, A’ is at the origin for any rotation about the origin.

Guided Practice – Algebraic Representations of Transformations – Page No. 300

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 21$

Answer: After a translation of 6 units to the right: X'(3, -2) Y'(5, 0) Z'(7, -6)

Question 2. Describe what happens to the x- and y-coordinates after a point is reflected across the x-axis. Type below: ____________

Answer: The x-coordinate remains the same, while the sign of the y-coordinate changes

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 22$

Answer: The triangle is rotated 90º clockwise about the origin

Question 4. How do the x- and y-coordinates change when a figure is translated right a units and down b units? Type below: ____________

Answer: The x-coordinates increase by a, and the y-coordinates decrease by b

9.4 Independent Practice – Algebraic Representations of Transformations – Page No. 301

Write an algebraic rule to describe each transformation.Then describe the transformation.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 23$

Answer: algebraic rule (x, y) -> (x-2, y-5) transformation translation of 2 units to the left and 5 units down new coordinates M'(-4, -2) N'(-2, -2) O'(-1, -4) P'(-4, -4)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 24$

Answer: algebraic rule (x, y) -> (-x, -y) transformation rotation of 180º new coordinates A'(0, 0) B'(0, -3) C'(2, -3) D'(2, 0)

Question 7. Triangle XYZ has vertices X(6, -2.3), Y(7.5, 5), and Z(8, 4). When translated, X′ has coordinates (2.8, -1.3). Write a rule to describe this transformation. Then find the coordinates of Y′ and Z′. Type below: ____________

Answer: algebraic rule (x, y) -> (x-3.2, y+1) new coordinates Y'(4.3, 6) Z'(4.8, 5)

Question 8. Point L has coordinates (3, -5). The coordinates of point L′ after a reflection are (-3, -5). Without graphing, tell which axis point L was reflected across. Explain your answer. ____________

Answer: Point L was reflected on the y-axis. When you reflect a point across the y-axis, the sign of the x-coordinate changes, and the sign of the y-coordinate remains the same

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 25$

Answer: The rectangle is translated 2 units to the left and 4 units down

Question 10. Parallelogram ABCD has vertices A(−2, −5$\frac{1}{2}$), B(−4, −5$\frac{1}{2}$),C(-3, -2), and D(-1, -2). Find the vertices of parallelogram A′B′C′D′ after a translation of 2 $\frac{1}{2}$ units down. Type below: __________

Answer: after a translation of 2 $\frac{1}{2}$ units A'(-2, -8) B'(-4, -8) C'(-3, -4 $\frac{1}{2}$) D'(-1, -4 $\frac{1}{2}$)

Algebraic Representations of Transformations – Page No. 302

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 26$

Answer: (x,y) –> (x+1,y-0.5) (x+1,y-0.5) –> (x+0.5,y-0.25)

Explanation: translation in units (x,y) –> (x+1,y-0.5) This step converts translation rule in units to translation rule in inches. (Divide by 2 since graph paper is half inch paper. (x+1,y-0.5) –> (x+0.5,y-0.25)

Question 12. Kite KLMN has vertices at K(1, 3), L(2, 4), M(3, 3), and N(2, 0). After the kite is rotated, K′ has coordinates (-3, 1). Describe the rotation, and include a rule in your description. Then find the coordinates of L′, M′, and N′. Type below: __________

Answer: rotation 90 counterclockwise rule (x, y) -> (-y, x) new coordinates L'(-4, 2) M'(-3, 3) N'(0, 2)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 27$

Answer: (-5, 5) has the same coordinates

Question 13. b. What is the equation of a line through the origin and this point? Type below: __________

Answer: x and y are equal so switching x and y has no effect on the coordinates

Question 13. c. Describe the transformation of the triangle. Type below: __________

Question 14. Critical Thinking Mitchell says the point (0, 0) does not change when reflected across the x- or y-axis or when rotated about the origin. Do you agree with Mitchell? Explain why or why not. _______

Answer: Yes, I agree with Mitchell

Explanation: Reflecting across the x-axis or y-axis changes the sign of the y or x coordinate 0 cannot change signs. Rotating about the origin does not change the origin (0, 0)

Question 15. Analyze Relationships Triangle ABC with vertices A(-2, -2), B(-3, 1), and C(1, 1) is translated by (x, y) → (x – 1, y + 3). Then the image, triangle A′B′C′, is translated by (x, y) → (x + 4, y – 1), resulting in A″B″C″. a. Find the coordinates for the vertices of triangle A″B″C″. Type below: __________

Answer: A”(-2-1+4, -2+3-1) = A”(1, 0) B”(-3-1+4, 1+3-1) = B”(0, 3) C”(1-1+4, 1+3-1) = C”(4, 3)

Question 15. b. Write a rule for one translation that maps triangle ABC to triangle A″B″C″. Type below: __________

Answer: (x, y) -> (x-1+4, y+3-1) (x, y) -> (x+3, y+2)

Guided Practice – Congruent Figures – Page No. 306

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 28$

Answer: A. After transformation (1, 3) (1, 4) (4, 4) (4, 3) B. After transformation (3, -1) (4, -1) (4, -4) (3, -4) C. After transformation (1, -1) (2, -1) (2, -4) (1, -4) D. After transformation (1, 1) (1, 2) (4, 2) (4, 1) E. After transformation (-6, -1) (-6, 0) (-3, 0) (-3, -1)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 29$

Question 2. What transformation is used to transform figure A into figure B? Type below: __________

Answer: Reflection across the y-axis

Explanation: Reflection across the y-axis is used to transform figure A into figure B

Question 3. What transformation is used to transform figure B into figure C? Type below: __________

Answer: Translation 3 units right and 4 units down

Explanation: Translation 3 units right and 4 units down is used to transform figure B into figure C

Question 4. What sequence of transformations is used to transform figure A into figure C? Express the transformations algebraically. Type below: __________

Answer: Reflection across the y-axis is used to transform figure A into figure B Translation 3 units right and 4 units down is used to transform figure B into figure C Algebraically: (x, y) -> (-x, y) (x, y) -> (x +3, y-4)

Question 5. Vocabulary What does it mean for two figures to be congruent? Type below: __________

Answer: Two figures are congruent when the figures have the same size and the same shape.

Question 6. After a sequence of translations, reflections, and rotations, what is true about the first figure and the final figure? Type below: __________

Answer: After a sequence of translations, reflections, and rotations, the first and final figures have the same size and shape. (They are congruent)

9.5 Independent Practice – Congruent Figures – Page No. 307

For each given figure A, graph figures B and C using the given sequence of transformations. State whether figures A and C have the same or different orientation.

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 30$

Answer: Different orientation

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 31$

Congruent Figures – Page No. 308

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 34$

Answer: From Site A to Site B: Translation 2 units right and 4 units down The size did NOT change The orientation changed

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 35$

Answer: From figure A to D: Reflection across the x-axis (-1, -5) (-1, -6) (2, -5) (4, -6) 90º clockwise rotation (4, -1) (5, -1) (5, -4) (4, -6) translation 6 units left (4, -1) (5, -1) (5, -4) (4, -6)

Question 13. Counterexamples The Commutative Properties for Addition and Multiplication state that the order of two numbers being added or multiplied does not change the sum or product. Are translations and rotations commutative? If not, give a counterexample. ________

Answer: No, Translation and rotations are not commutative

Explanation: The point (2, 2) becomes (2, -4) when translated 2 units to the right then rotated 90 around the origin. The point (2, 2) becomes (4, -2) when rotated 90 around the origin then translated 2 units to the right. The above two points are not the same.

Question 14. Multiple Representations For each representation, describe a possible sequence of transformations. a. (x, y) → (-x – 2, y + 1) Type below: ____________

Answer: translation 2 units right and 1 unit up reflection across y-axis

Question 14. b. (x, y) → (y, -x – 3) Type below: ____________

Answer: rotation 90º clockwise around the origin translation 3 units down

Ready to Go On? – Model Quiz – Page No. 309

9.1–9.3 Properties of Translations, Reflections, and Rotations

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Model Quiz img 36$

Answer: After translation: A'(2, 1) B'(2, -1) C'(5, -1)

Question 2. On the same coordinate grid, graph the image of triangle ABC after a reflection across the x-axis. Label the vertices of the image A”, B”, and C”. Type below: ____________

Answer: After reflection: A”(-4, -5) B”(-4, -3) C”(-1, -3)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Model Quiz img 37$

Answer: After rotation: H'(0, -4) I'(0, -1) J'(2, -2) K'(2, -3)

9.4 Algebraic Representations of Transformations

Question 4. A triangle has vertices at (2, 3), (−2, 2), and (−3, 5). What are the coordinates of the vertices of the image after the translation (x, y) → (x + 4, y − 3)? Type below: ____________

Answer: After translation: (6, 0) (2, -1) (1, 2)

9.5 Congruent Figures

Question 5. Vocabulary Translations, reflections, and rotations produce a figure that is _____ to the original figure. Type below: ____________

Explanation: Vocabulary Translations, reflections, and rotations produce a figure that is congruent to the original figure.

Question 6. Use the coordinate grid for Exercise 3. Reflect H’I’J’K’ over the y-axis, then rotate it 180° about the origin. Label the new figure H″I″J″K″. Type below: ____________

Answer: after reflection H'(0, -4) I'(0, -1) J'(-2, -2) K'(-2, -3) after rotation H”(0, 4) I”(0, 1) J”(2, 2) K”(2, 3)

ESSENTIAL QUESTION

Question 7. How can you use transformations to solve real-world problems? Type below: ____________

Answer: Transformational properties allow the systematic movement of congruent figures while maintaining or adjusting their orientation.

Selected Response – Mixed Review – Page No. 310

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Mixed Review img 38$

Answer: c. C

Explanation: After a translation of 8 units right and 3 units up, the orientation of figure L stays the same.

Question 2. Figure A is reflected over the y-axis and then lowered 6 units. Which sequence describes these transformations? Options: a. (x, y) -> (x, -y) and (x, y) -> (x, y – 6) b. (x, y) -> (-x, y) and (x, y) -> (x, y – 6) c. (x, y) -> (x, -y) and (x, y) -> (x – 6, y) d. (x, y) -> (-x, y) and (x, y) -> (x – 6, y)

Answer: b. (x, y) -> (-x, y) and (x, y) -> (x, y – 6)

Explanation: reflection over y-axis: (x, y) -> (-x, y) Translation 6 units down (x, y) -> (x, y-6)

$Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Mixed Review img 39$

Answer: d. IV

Explanation: After a rotation of 90° counterclockwise about the origin, the triangle will be in QIV

Question 4. Which rational number is greater than −3 $\frac{1}{3}$ but less than −$\frac{4}{5}$? Options: a. −0.4 b. −$\frac{9}{7}$ c. −0.19 d. −$\frac{22}{5}$

Answer: b. −$\frac{9}{7}$

Question 5. Which of the following is not true of a trapezoid that has been reflected across the x-axis? Options: a. The new trapezoid is the same size as the original trapezoid. b. The new trapezoid is the same shape as the original trapezoid. c. The new trapezoid is in the same orientation as the original trapezoid. d. The x-coordinates of the new trapezoid are the same as the x-coordinates of the original trapezoid.

Answer: d. The x-coordinates of the new trapezoid are the same as the x-coordinates of the original trapezoid.

Explanation: The x-coordinates of the new trapezoid are the same as the x-coordinates of the original trapezoid.

Question 6. A triangle with coordinates (6, 4), (2, −1), and (−3, 5) is translated 4 units left and rotated 180° about the origin. What are the coordinates of its image? Options: a. (2, 4), (-2, -1), (-7, 5) b. (4, 6), (-1, 2), (5, -3) c. (4, -2), (-1, 2), (5, 7) d. (-2, -4), (2, 1), (7, -5)

Answer: d. (-2, -4), (2, 1), (7, -5)

Question 7. A rectangle with vertices (3, -2), (3, -4), (7, -2), (7, -4) is reflected across the x-axis and then rotated 90° counterclockwise. a. In what quadrant does the image lie? ____________

Answer: After reflection and rotation, the image lies in QII

Question 7. b. What are the vertices of the image? Type below: ____________

Answer: image vertices (-2, 3) (-4, 3) (-2, 7) (-4, 7)

Question 7. c. What other transformations produce the same image? Type below: ____________

Answer: A reflection across the y-axis and 90º clockwise rotation will produce the same result.

Conclusion:

The Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence pdf are available both online and offline. We have provided in pdf format so that students can practice the problems offline. We know that maths is the scoring and also typical among all the subjects. But you can make it easy if you understand the concept of the chapter. Students can refer to the Go Math Grade 8 Answer Key in their convenient way. Practice well and make maths your favorite subject. Best of Luck!!!