Name_____________________________________Date________________Period_______SCORE_______

Unit 8 Test Review- Geometry I: Transformations, Congruence and Similarity

Directions: Choose the correct term or phrase to complete each sentence or answer the questions.

1. A (transformation, translation) maps one figure onto another. 2. The original figure before a transformation is called a(n) (image, preimage). 3. The fixed point around which shapes more in a circular motion is the center of (dilation, rotation). 4. The figure after a transformation is called an (image, preimage). 5. When a mirror image is produced by flipping a figure over a line, it is a (reflection, rotation). 6. A (dilation, reflection) is the image produced when a figure is enlarged or reduced. 7. Figures that have the same size and shape are (congruent, similar) figures. 8. When a figure is moved without turning it, it is called a (rotation, translation). 9. Define a transformation using pre-image and image. 10. Define rotation and give the coordinate rules when a figure is rotated clockwise around origin for a 90°, 180°, and 270°. 11. Define compositions of transformations. 12. Define Similar. 13. Define Scale Factor. 14a. Define Corresponding Parts. 14b. Name the rigid transformations

Answers: 1._________________ 2._________________ 3._________________ 4. ________________ 5._________________ 6.__________________ 7.___________________ 8.___________________ 9.______________________________________ 10.______________________________________ 11.______________________________________ 12.______________________________________ 13.______________________________________ 14a._____________________________________ 14b._____________________________________

15. Given the coordinate rule (x + 4, y + 3), translate the ΔNBY. Label the ΔN’B’Y’. Then write the new coordinates.

16. The quadrilateral JANT has been translated. Write the coordinate rule for this translation.

17. Reflect the quadrilateral IMTY over the x-axis. Label the new quadrilateral I’M’T’Y’. Write the new coordinates.

Answers: 15 N’___________________ B’___________________ Y’___________________ 16.__________________ 17 T’___________________ I’___________________ M’___________________ Y’___________________

18. Reflect the following image over the line x=1. Relabel and write the coordinates.

19. Draw the line of reflection that would reflect each figure. a. Write the equation for the line of reflection. b. Write a coordinate rule for the reflection. i. ii.

20. Rotate the following image 270⁰ clockwise about the origin.a. Write a coordinate rule for the rotation. b. Compare the slopes of the segments of the pre-image to the image.

Answers 18. Q’__________________ W’__________________ V’___________________ A’___________________ 19i) a._______________ b.______________ 19ii) a._______________ b._______________

20a.___________________

b.____________________

21. Rotate the following image 90⁰ counter clockwise about point F. Draw and label the image and write the new coordinates.

Directions: For each of the following rotations, the center of rotation is the origin. Determine the angle of rotation (be sure to also indicate a direction of rotation). Write a coordinate rule for the transformation. 22. 23.

24. Dilatethefollowingshape. 25.DilatethefollowingUsethescalefactor3,andthe shape.Usethescalefactorcenterofdilation(0,0). ½.ThecenterofdilationWritethenewcoordinates. isat(8,6).Writethenew coordinates.

Answers: 21. F’_____________________ Q’____________________ A’_____________________ U’_____________________ 22. Angle of rotation: ___________________ Coordinate Rule: ____________________ 23. Angle of rotation: ___________________ Coordinate Rule: ____________________ 24. R’_____________________ S’_____________________ T’_____________________ U’_____________________ 25. R’_____________________ S’____________________ T’_____________________

26. The following shapes have been dilated. Find the center of dilation and the scale factor. For b write a coordinate rule.

a.b.

27. Δ𝐴𝐵𝐶 has been plotted below.

a. Reflect Δ𝐴𝐵𝐶 over the y-axis and label the image Δ𝐴′𝐵′𝐶′. b. Reflect Δ𝐴′𝐵′𝐶′ over the x-axis and label the image Δ𝐴′′𝐵′′𝐶′′. c. What one transformation is the same as this double reflection? 28. The two objects below are congruent.

a. Describe the transformation or sequence of transformations that will carry ΔXYZ onto ΔPRQ. b. List the congruent corresponding parts. c. Write a congruence statement for the triangles.

Answers: 26a. ScaleFactor: ___________________ Center of dilation: __________________ 26b. Scale Factor: ________________ Center of dilation: __________________ Coordinate Rule: ___________________ 27a._________________ b._________________ c._________________ 28a._________________ 28b._________________ 28c._________________

29. The triangles below are similar. a. List the sequence of transformations that verifies the similarity of the two figures. b. Write a similarity statement for the triangles.

30. Determine whether the figures below are congruent, similar, or neither. Provide a justification for your answer.

31. Determine whether the following transformations or sequence of transformations will result in similar figures, congruent figures, or neither. Provide a justification for your answer. a. (𝑥, 𝑦) → (2𝑥 +2, 𝑦 + 2) b. (𝑥, 𝑦) → (y, -x) followed by (𝑥, 𝑦) → (2𝑥, 2𝑦) c. (𝑥, 𝑦) → (2𝑥, 3𝑦) followed by a reflection across the x-axis d. (𝑥, 𝑦) → (𝑥 + 5, 𝑦 + 5) followed by a 90˚ rotation counterclockwise about the origin e. (𝑥, 𝑦) → (!

!𝑥, !!𝑦) followed by (𝑥, 𝑦) → (-𝑦, 𝑥)

f. (𝑥, 𝑦) → (𝑥, 𝑦 + 4) followed by a 180˚ rotation clockwise about the origin.

Answers: 29a._________________ 29b._________________ 30. _________________ 31a._________________ 31b._________________ 31c._________________ 31d._________________ 31e._________________ 31f._______________

32.

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35.