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Geometry 9-5 Complete Lesson: Congruence Transformations

By Matt Richardson
Last updated over 2 years ago
20 Questions
Note 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.
1.

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.

Problem 1 Got It?

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3.

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

  • ABCD
  • UVW
  • JKHI
  • MNQ
4.

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.

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.

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6.

Problem 3 Got It?

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7.

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

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8.

Problem 5 Got It? Are the figures congruent?

10.
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12.

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.

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

14.

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.

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'
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16.

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.

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

18.

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.

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

20.

Reflection: Math Success

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