1. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Warm-Up Reflect this triangle over the y-axis and then translate it up 2 units. What are the coordinates of the new vertices?

2. Congruence in Terms of Transformations Essential Question: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes.

3. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. In order for two figures to be congruent every side and angle of the pre-image must be exactly the same as a side or angle in the image.

4. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. You can show that two figures are congruent if you can show that you can carry one onto the other through a series of transformation (translation, rotation, and/or reflection).

5. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Examples: Two rectangles are shown on the coordinate plane below. Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select three that apply. A) The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2. B) The rectangles are congruent since a reflection over the x–axis followed by a translation of 7 units to the right carries Rectangle 1 onto Rectangle 2. C) The rectangles are congruent since a reflection over the y–axis followed by a translation of 1 unit to the right and 6 units up carries Rectangle 1 onto Rectangle 2. D) The rectangles are congruent since a rotation of 180° clockwise about the origin followed by a translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2.

6. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Examples: Two rectangles are shown on the coordinate plane below. Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select three that apply. A) The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2.

7. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Examples: Two rectangles are shown on the coordinate plane below. Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select three that apply. C) The rectangles are congruent since a reflection over the y–axis followed by a translation of 1 unit to the right and 6 units up carries Rectangle 1 onto Rectangle 2.

8. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Examples: Two rectangles are shown on the coordinate plane below. Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select three that apply. D) The rectangles are congruent since a rotation of 180° clockwise about the origin followed by a translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2.

9. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Figures 1 and 2 are shown in the coordinate plane below. Part A: Is there a sequence of rigid motions that takes Figure 1 onto Figure 2? Explain your reasoning.

10. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Part B: Based on your response to Part A, are the two figures congruent? Explain your reasoning.

11. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. If ΔTUV is translated to image ΔT'U'V', as shown below, by the rule (x, y) → (x + 8, y – 3), what are the coordinates of ΔTUV?

12. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Directions: In the images below decide if the two figures are congruent. If they are tell the transformation(s) that takes one figure to the other. If they are not explain why not. HINT: Write the coordinates of each image. A B C A’ B’ C’

13. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Directions: In the images below decide if the two figures are congruent. If they are tell the transformation(s) that takes one figure to the other. If they are not explain why not. HINT: Write the coordinates of each image. A A’ B B’ C C’ D D’

14. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Directions: In the images below decide if the two figures are congruent. If they are tell the transformation(s) that takes one figure to the other. If they are not explain why not. HINT: Write the coordinates of each image.

15. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Directions: In the images below decide if the two figures are congruent. If they are tell the transformation(s) that takes one figure to the other. If they are not explain why not. HINT: Write the coordinates of each image.

16. EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Homework: Page 279 #1-7 and Page 285 #27-29