1. Use the SSS Postulate to test for triangle congruence.
Use the SAS Postulate to test for triangle congruence.
Splash Screen

2. G.CO.10 Prove theorems about triangles.
Content Standards
G.CO.10 Prove theorems about triangles.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
1 Make sense of problems and persevere in solving them.
CCSS

3. included angle
Vocabulary

4. Concept 1

5. Write a proof. ___ Given: QU  AD, QD  AU Prove: ΔQUD  ΔADU
Use SSS to Prove Triangles Congruent
Write a proof.
Given: QU  AD, QD  AU
___
Prove: ΔQUD  ΔADU
Example 1

6. Given: AC  AB D is the midpoint of BC. Prove: ΔADC  ΔADB ___
Example 1 CYP

7. SSS on the Coordinate Plane
EXTENDED RESPONSE Triangle DVW has vertices D(–5, –1), V(–1, –2), and W(–7, –4). Triangle LPM has vertices L(1, –5), P(2, –1), and M(4, –7). a. Graph both triangles on the same coordinate plane. b. Use your graph to make a conjecture as to whether the triangles are congruent. Explain your reasoning. c. Write a logical argument that uses coordinate geometry to support the conjecture you made in part b.
Example 2A

8. SSS on the Coordinate Plane
Read the Test Item You are asked to do three things in this problem. In part a, you are to graph ΔDVW and ΔLPM on the same coordinate plane. In part b, you should make a conjecture that ΔDVW  ΔLPM or ΔDVW  ΔLPM based on your graph. Finally, in part c, you are asked to prove your conjecture. /
Solve the Test Item a.
Example 2B

9. SSS on the Coordinate Plane
b. From the graph, it appears that the triangles have the same shapes, so we conjecture that they are congruent.
c. Use the Distance Formula to show all corresponding sides have the same measure.
Example 2C

10. SSS on the Coordinate Plane
Example 2C

11. SSS on the Coordinate Plane
Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔDVW  ΔLPM by SSS.
Example 2 ANS

12. Determine whether ΔABC  ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).
Example 2A

13. Concept 2

14. Use SAS to Prove Triangles are Congruent
ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG  ΔHIG if EI  FH, and G is the midpoint of both EI and FH.
Example 3

15. Given: EI  FH; G is the midpoint of both EI and FH.
Use SAS to Prove Triangles are Congruent
Given: EI  FH; G is the midpoint of both EI and FH.
Prove: ΔFEG  ΔHIG
Proof:
Reasons
Statements
Example 3

16. Write a proof to prove that ΔABG  ΔCGB if ABG  CGB and AB  CG
Write a proof to prove that ΔABG  ΔCGB if ABG  CGB and AB  CG. Choose the best reason to fill in the blank.
Reasons
Proof:
Statements
Example 3

17. Use SAS or SSS in Proofs
Write a proof.
Prove: Q  S
Example 4

18. Homework
Page 269 (5, 6, 9, 12, 13)
Concept 1