Lesson 12

Congruent Polygons

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Problem 1

  1. Show that the two pentagons are congruent.
  2. Find the side lengths of \(ABCDE\) and the angle measures of \(FGHIJ\).
Two figures A B C D E and F G H I J on a square grid.

Solution

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Problem 2

For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.

  1.  
    Two quadrilaterals A B C D and E F G H on a square grid.
  2.  
    Two figures A B C D E F and G H I J K L on a coordinate plane, origin O.
  3.  
    Two circles A and B on a coordinate plane, origin O.

Solution

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Problem 3

  1. Draw segment \(PQ\).
  2. When \(PQ\) is rotated \(180^\circ\) around point \(R\), the resulting segment is the same as \(PQ\). Where could point \(R\) be located?

Solution

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(From Unit 1, Lesson 8.)

Problem 4

Here is trapezoid \(ABCD\).

Trapezoid \(A\ B\ C\ D\). Upper and lower sides are parallel. Upper and lower left angles are right angles. Upper right angle is 120 degrees and lower right angle is 60 degrees.

 

Using rigid transformations on the trapezoid, build a pattern. Describe some of the rigid transformations you used.

Solution

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(From Unit 1, Lesson 10.)