Lesson 11

Congruence

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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

These two figures are congruent, with corresponding points marked.

Transformation quadrilaterals.
  1. Are angles \(ABC\) and \(A'B'C'\) congruent? Explain your reasoning.
  2. Measure angles \(ABC\) and \(A’B’C’\) to check your answer.

Solution

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Problem 3

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 4

Which of these four figures are congruent to the top figure?

Five quadrilateral figures each with 3 blue dots.
A:

A

B:

B

C:

C

D:

D

Solution

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Problem 5

Here are two figures.

Two figures, A and B. Figure A is an oval, wider than is tall. Figure B appears circular.

Show, using measurement, that these two figures are not congruent.

Solution

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