Geometry 9-5 Complete Lesson: Congruence Transformations

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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?

10

Problem 1 Got It?

G.CO.7

5

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

ABCD

10

G.CO.7

10

Problem 3 Got It?

G.CO.7

30

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

G.CO.7

G.CO.8

5

Problem 5 Got It? Are the figures congruent?

15

10

G.CO.7

10

G.CO.7

10

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?

10

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

10

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.

10

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)

A'

G.CO.6

10

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

10

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

10

∠B

10

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

10

Reflection: Math Success

G.CO.7

Geometry 9-5 Complete Lesson: Congruence Transformations

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?

Problem 1 Got It?

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

Problem 3 Got It?

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

Problem 5 Got It? Are the figures congruent?

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?

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

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.

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.

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.

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

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

Reflection: Math Success

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?

Problem 1 Got It?

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

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.

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.

Problem 3 Got It?

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

Problem 5 Got It? Are the figures congruent?

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?

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

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.

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.

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.

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

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

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

Reflection: Math Success

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.

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.

Geometry 9-5 Complete Lesson: Congruence Transformations

Geometry 9-5 Complete Lesson: Congruence Transformations

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?

Problem 1 Got It?

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

Problem 3 Got It?

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

Problem 5 Got It? Are the figures congruent?

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?

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

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.

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.

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.

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

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

Reflection: Math Success

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?

Problem 1 Got It?

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

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.

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.

Problem 3 Got It?

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

Problem 5 Got It? Are the figures congruent?

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?

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

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.

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.

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.

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

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

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

Reflection: Math Success

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.

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.

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

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