6.3(b) Notes: Proving Triangles Congruent - SAS   Lesson Objective: Use the SAS Postulate to test for triangle congruence. CCSS: G.CO.10, G.SRT.5 You will need: CPR, colored pens

Lesson 1: SAS Congruence   Draw 2 line segments vertically to use for measurement guides: 1.25” and 2.5”. 1.25” 2.5”

Lesson 1: SAS Congruence   Construct ∆ABC with base AC 2.5” and left side AB 1.25”, with m/ A = 50°. 1.25” 2.5” A 2.5” C

Lesson 1: SAS Congruence   Construct ∆ABC with base AC 2.5” and left side AB 1.25”, with m/ A = 50°. 1.25” 50° 1.25” 2.5” A 2.5” C

Lesson 1: SAS Congruence Connect B to C.   Connect B to C. B 1.25” 50° 1.25” 2.5” A 2.5” C

Lesson 1: SAS Congruence   Construct ∆DEF with base DF 2.5” and right side DE 1.25”, with m/ D = 50°. 1.25” 50° 1.25” 2.5” F 2.5” D

Lesson 1: SAS Congruence Connect E to F.   Connect E to F. E 1.25” 50° 1.25” 2.5” F 2.5” D

Lesson 1: SAS Congruence   Construct ∆GHJ with base GJ 2.5” and left side GH 1.25”, with m/ G = 120°. 1.25” 2.5” G 2.5” J

Lesson 1: SAS Congruence   Construct ∆GHJ with base GJ 2.5” and left side GH 1.25”, with m/ G = 120°. H 1.25” 120° 1.25” 2.5” G 2.5” J

Lesson 1: SAS Congruence Connect H to J.   Connect H to J. H 1.25” 120° 1.25” 2.5” G 2.5” J

Lesson 1: SAS Congruence Which triangles are congruent? Why? B 1.25”   Which triangles are congruent? Why? B 1.25” 50° E A 2.5” C 1.25” 50° F 2.5” D H 120° G 2.5” J

Lesson 1: SAS Congruence   What if the third one is rotated around? Which tri-angles are congruent? B 1.25” 50° E A 2.5” C 1.25” 50° F 2.5” D G 2.5” 120° 1.25” J H

Side-Angle-Side (SAS) Congruence: If 2 sides and the included Side-Angle-Side (SAS) Congruence: If 2 sides and the included* angle of one ∆ are congru-ent to 2 sides and the included* angle of another ∆, the ∆s are congruent.   * included means “in between” B ∆ABC ∆DEF E 1.25” 1.25” 50° 50° A 2.5” C F 2.5” D

Lesson 2: Using SAS W of XV and WY. Use SAS to prove ∆XYZ ∆VWZ. V X Z   Given Z is the midpoint of XV and WY. Use SAS to prove ∆XYZ ∆VWZ. V X Z Y Statement Reason S1 1. A 2. S2 3. 4.

Lesson 3: Proving ∆s Using SAS Prove: ∆EGF ∆HFG Given: l| |m, EG HF Prove: ∆EGF ∆HFG Statement Reason S1 1. A 2. S2 3. 4.

6.3: Do I Get It? Yes or No Write a two-column proof for each. 1. 2. Given: BC| |AD, BC AD Prove: ∆ABD ∆CDB B C     A D