Congruent Figures

Slide 4-2

Definitions

Congruent figures have the exact same shape and
size. All the figures below are congruent. As shown
below, a flip, rotate (turn), or slide does not affect
whether figures are congruent because they still
have the same shape and size.

Copyright © 2014 Pearson Education, Inc.

Slide 4-3

Definitions

When figures are congruent, their corresponding
sides are congruent, and their corresponding angles
are congruent.

Copyright © 2014 Pearson Education, Inc.

Corresponding Angles
& Sides

Slide 4-4

ExampleNaming Congruent Parts

For the two figures, we
are given that ABCD ≅TRQS.
Solution
The figures help, but having the congruent angles
listed in the corresponding order is all that is needed.
ABCD ≅TRQS
Angles:
Sides:

Copyright © 2014 Pearson Education, Inc.

Slide 4-5

Example
Using Congruent Triangles to

Find Angle Measures

In the process of folding an origami cat, two
congruent triangles are formed.
Given that ΔABC ≅ ΔAEF, |
find m∠F.
Solution
m∠C + 96° + 36° = 180°

m∠C = 48°

Since ΔABC ≅ ΔAEF,

m∠F = m∠C = 48°

Copyright © 2014 Pearson Education, Inc.

Slide 4-6

Theorem 4.2-1 Third Angles Theorem

Copyright © 2014 Pearson Education, Inc.

Slide 4-7

Example
Using the Third Angles Theorem

Find the value of x.
Solution
From the figures, we have
∠J ≅∠R and ∠H ≅∠S.
Thus, from the Third Angles Theorem,
∠K ≅∠Q or m∠K= m∠Q.
Use ΔJHK to find m∠K.
m∠K= 180° – 53° – 92° = 35°

Copyright © 2014 Pearson Education, Inc.

Slide 4-8

Example
Using the Third Angles Theorem

Find the value of x.
Solution
m∠K= m∠Q
35 = 10x + 5
30 = 10x
3 = x
The value of x is 3. To check, replace x with 3 and
see that 10x + 5 = 35. Then make sure that
53° + 92° + 35° = 180°.

Copyright © 2014 Pearson Education, Inc.

Slide 4-9

ExampleProving Triangles Are Congruent

Given: segments LM ≅LO, MN ≅ON,
∠M ≅∠O, ∠MLN ≅∠OLN
Prove: ΔLMN ≅ ΔLON

Copyright © 2014 Pearson Education, Inc.

Slide 4-10

ExampleProving Triangles Are Congruent

Copyright © 2014 Pearson Education, Inc.

Statements

Reasons

1. Given

2. Reflexive Property of Congruence

3. Given

4. Third Angles Theorem

5. Definition of congruent
triangles