1. 2.2 Proofs Involving Congruence
CHAPTER
2.2 Proofs Involving Congruence
Copyright © 2014 Pearson Education, Inc.

2. Copyright © 2014 Pearson Education, Inc.
Congruent Segments
Two segments that have the same length are called congruent segments. The symbol ≅ means congruent. We mark congruent segments in a figure with exactly the same number of tick marks.
Copyright © 2014 Pearson Education, Inc.

3. Copyright © 2014 Pearson Education, Inc.
Definition
Two angles that have the same measure are called congruent angles. Recall that the symbol ≅ means congruent. We mark congruent angles with exactly the same number of arcs, as shown in the figures below.
Copyright © 2014 Pearson Education, Inc.

4. Copyright © 2014 Pearson Education, Inc.
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.

5. Copyright © 2014 Pearson Education, Inc.
Definitions
When figures are congruent, their corresponding sides are congruent, and their corresponding angles are congruent.
Corresponding Angles & Sides
Copyright © 2014 Pearson Education, Inc.

6. Naming 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.

7. Proving Triangles Are Congruent
Given: segments LM ≅ LO, MN ≅ ON, ∠M ≅ ∠O, ∠MLN ≅ ∠OLN Prove: ΔLMN ≅ ΔLON
Copyright © 2014 Pearson Education, Inc.

8. Proving Triangles Are Congruent
Statements
Reasons
1. Given
2. Reflexive Property of Congruence
3. Given
4. Third Angles Theorem
5. Definition of congruent triangles
Copyright © 2014 Pearson Education, Inc.

9. Postulate 4.3-2 Side-Angle-Side (SAS) Postulate
Copyright © 2014 Pearson Education, Inc.

10. Proving Triangles Are Congruent
Given: The figure with congruent segments shown by equal number of tick marks Prove:
Statements
Reasons
1. Given
2. Vertical Angles Theorem
3. SAS Postulate
Copyright © 2014 Pearson Education, Inc.

11. Postulate 4.4-1 Angle-Side-Angle (ASA) Postulate
Copyright © 2014 Pearson Education, Inc.

12. Copyright © 2014 Pearson Education, Inc.
Identifying ASA
Multiple Choice: Choose two triangles that are congruent by the ASA Postulate. Explain why. a. b. c. d. Solution Choices b and d are congruent by ASA because for these two triangles, the sides marked congruent are the included sides of the two congruent angles.
Copyright © 2014 Pearson Education, Inc.

13. Postulate 4.3-1 Side-Side-Side (SSS) Postulate
Copyright © 2014 Pearson Education, Inc.

14. Proving Triangles Are Congruent
Given: Prove:
Statements
Reasons
1. Given
2. Reflexive Property of Congruence
3. SSS Postulate
Copyright © 2014 Pearson Education, Inc.