1. 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

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

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

4. 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” ” A ” C

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

6. 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” ” F ” D

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

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

9. 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” ” G ” J

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

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

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

13. 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” ”
50° °
A ” C F ” D

14. 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.

15. 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.

16. 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