1. Proving Congruence: SSS and SAS
Lesson 4-4
Proving Congruence: SSS and SAS

2. Standardized Test Practice:
Transparency 4-4
5-Minute Check on Lesson 4-3
Refer to the figure.
1. Identify the congruent triangles.
2. Name the corresponding congruent
angles for the congruent triangles.
3. Name the corresponding congruent sides for the congruent triangles.
4. Find x.
5. Find mA.
Find mP if OPQ  WXY and mW = 80, mX = 70, mY = 30.
Standardized Test Practice: A
30 B
70 C
80 D
100

3. Standardized Test Practice:
Transparency 4-4
5-Minute Check on Lesson 4-3
Refer to the figure.
1. Identify the congruent triangles.
LMN  RTS
2. Name the corresponding congruent
angles for the congruent triangles.
L  R, N  S, M  T
3. Name the corresponding congruent sides for the congruent triangles.
LM  RT, LN  RS, NM  ST
4. Find x. 3
5. Find mA. 63
Find mP if OPQ  WXY and mW = 80, mX = 70, mY = 30.
Standardized Test Practice: A
30 B
70 C
80 D
100

4. Objectives Use the SSS Postulate to test for triangle congruence
Use the SAS Postulate to test for triangle congruence

5. Vocabulary
Included angle – the angle formed by two sides sharing a common end point (or vertex)

6. Postulates
Side-Side-Side (SSS) Postulate: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

7. Side – Angle – Side (SAS)
Given: AC = CD
BC = CE
Prove: ABC = DEC
BC = CE Given
ACB  DCE (included angle)
AC = CD Given in problem
Statements
Reasons
Vertical Angles Theorem
ABC  DEC
SAS Postulate

8. ENTOMOLOGY The wings of a moth form two triangles
ENTOMOLOGY The wings of a moth form two triangles. Write a two-column proof to prove that FEG  HIG if EI  FH, FE  HI, and G is the midpoint of both EI and FH.
Given: EI  FH; FE  HI; G is the midpoint of both EI and FH.
Prove: FEG  HIG
1. Given 1.
Proof:
Reasons
Statements
2. Midpoint Theorem 2.
3. SSS
3. FEG HIG

9. Write a two-column proof to prove that ABC GBC if
3. SSS
1. Given
2. Reflexive
Proof:
Reasons
Statements 1. 2.
3. ABC GBC

10. COORDINATE GEOMETRY Determine whether WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain.
Use the Distance Formula to show that the corresponding sides are congruent.

11. Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS.

12. Determine whether ABC DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.
Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, ABC DEF by SSS.

13. Write a flow proof.
Given:
Prove: QRT STR
Answer:

14. Write a flow proof.
Given:
Prove: ABC ADC
Proof:

15. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
Two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle. The triangles are congruent by SAS.
Answer: SAS

16. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
Each pair of corresponding sides are congruent. Two are given and the third is congruent by Reflexive Property. So the triangles are congruent by SSS.
Answer: SSS

17. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. a.
Answer: SAS

18. b.
Answer: not possible

19. Summary & Homework Summary: Homework:
If all of the corresponding sides of two triangles are congruent, then the triangles are congruent (SSS).
If two corresponding sides of two triangles and the included angle are congruent, then the triangles are congruent (SAS).
Homework:
pg : 6-8, 17, 22-25, 33-34