#### Transcript Geometry Section 2.2 Notes

CHAPTER 2 2.2 Proofs Involving Congruence Copyright © 2014 Pearson Education, Inc. Slide 4-1 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. Slide 4-2 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. Slide 4-3 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 4-4 Definitions When figures are congruent, their corresponding sides are congruent, and their corresponding angles are congruent. Corresponding Angles & Sides AB RS A R B S C T Copyright © 2014 Pearson Education, Inc. BC ST CA TR Slide 4-5 Example 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: A T , B R, C Q, D S Sides: AB TR, BC RQ, CD QS , DA ST Copyright © 2014 Pearson Education, Inc. Slide 4-6 Example Proving Triangles Are Congruent Given: segments LM ≅ LO, MN ≅ ON, ∠M ≅ ∠O, ∠MLN ≅ ∠OLN Prove: ΔLMN ≅ ΔLON Copyright © 2014 Pearson Education, Inc. Slide 4-7 Example Proving Triangles Are Congruent Statements Reasons 1. LM LO, MN ON 1. Given 2. LN LN 2. Reflexive Property of Congruence 3. M O , MLN OLN 3. Given 4. MNL ONL 4. Third Angles Theorem 5. LMN LON 5. Definition of congruent triangles Copyright © 2014 Pearson Education, Inc. Slide 4-8 Postulate 4.3-2 Side-Angle-Side (SAS) Postulate Copyright © 2014 Pearson Education, Inc. Slide 4-9 Example Proving Triangles Are Congruent Given: The figure with congruent segments shown by equal number of tick marks Prove: ABE CBD Statements Reasons 1. AB BC, EB BD 1. Given 2. 1 2 2. Vertical Angles Theorem 3. ABE CBD 3. SAS Postulate Copyright © 2014 Pearson Education, Inc. Slide 4-10 Postulate 4.4-1 Angle-Side-Angle (ASA) Postulate Copyright © 2014 Pearson Education, Inc. Slide 4-11 Example 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. Slide 4-12 Postulate 4.3-1 Side-Side-Side (SSS) Postulate Copyright © 2014 Pearson Education, Inc. Slide 4-13 Example Proving Triangles Are Congruent Given: AB CD, AC BD Prove: ABC DCB Statements Reasons 1. AB CD, AC BD 1. Given 2. CB CB 2. Reflexive Property of Congruence 3. ABC DCB 3. SSS Postulate Copyright © 2014 Pearson Education, Inc. Slide 4-14