Geometry 9-5 Congruence Transformations

by Matthew Richardson

| 20 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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1

10 pts

Solve It! Suppose that you want to create two identical wings for a model airplane. You draw one wing on a large sheet of tracing paper, fold it along the dashed line, and then tract the first wing. How do you know that the two wings are identical?

2

2

10 pts

Problem 1 Got It?

A

B

C

D

3

4

5

3

5 pts

Problem 2 Got It? Match congruent pairs of figures from the grid.

- ABCD
- UVW

- JKHI
- MNQ

4

10 pts

Problem 2 Got It? What is a sequence of rigid motions that maps ABCD to JKHI? Write your response using either sentences or transformation notation.

5

10 pts

Problem 2 Got It? What is a sequence of rigid motions that maps MNQ to UVW? Write your response using either sentences or transformation notation.

6

6

10 pts

Problem 3 Got It?

A

B

C

D

7

30 pts

Problem 4 Got It? Complete a proof to verify the SSS postulate on the canvas.

8

9

8

5 pts

Problem 5 Got It? Are the figures congruent?

Yes

No

10

10

10 pts

A

B

C

D

11

11

10 pts

A

B

C

D

12

10 pts

Reasoning: How can the definition of congruence in terms of rigid motions be more useful than a definition of congruence that relies on corresponding angles and sides?

13

10 pts

Reasoning: Is a composition of a rotation followed by a glide reflection a congruence transformation? Explain.

14

10 pts

Open-Ended: What is an example of a board game in which a piece is moved using a congruence transformation? Describe the congruence transformation in the context of the game.

15

10 pts

Review Lesson 9-4: A triangle has vertices A(3, 2), B(4, 1), and C(4, 3). Find the coordinates of the images of A, B, and C for a glide reflection with translation (x, y) → (x, y + 1) and reflection line x = 0.

- (3, 3)
- (-4, 4)
- (4, -2)
- (-3, 3)
- (-4, 2)
- (-4, 3)

- A'
- B'
- C'

16

10 pts

Review Lesson 5-6: The lengths of two sides of a triangle are given in the column on the right. Identify the range of possible lengths of the third side of each triangle.

- 3.5 < x <12.5
- 10 < x < 42
- 0 < x < 18
- 1 < x < 40

- 16, 26
- 19.5, 20.5
- 9, 9
- 4.5, 8

17

10 pts

Review Lesson 7-2: Determine the scale drawing dimensions of the room using a scale of ¼ in. = 1 ft.

kitchen: 12 ft by 16 ft

4 ft by 5 ft 4 in.

3 ft by 4 ft

25 in. by 48 in.

3 in. by 4 in.

18

18

10 pts

Vocabulary Review: △ABC ≅ △DEF. Match the corresponding parts from each triangle.

- ∠B
- side AB
- side BC
- ∠F
- side CA

- side DE
- ∠C
- ∠E
- side EF
- side FD

19

10 pts

Use Your Vocabulary: Which transformations make up a glide reflection? Select all that apply.

translation

reflection

rotation

dilation

20

10 pts

Reflection: Math Success

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