1. Five-Minute Check (over Lesson 4–2) Mathematical Practices Then/Now
New Vocabulary
Postulate 4.1: Side-Side-Side (SSS) Congruence
Example 1: Use SSS to Prove Triangles Congruent
Example 2: SSS on the Coordinate Plane
Postulate 4.2: Side-Angle-Side (SAS) Congruence
Example 3: Real World Example: Use SAS to Prove Triangles Are Congruent
Example 4: Use SAS or SSS in Proofs
Lesson Menu

2. Write a congruence statement for the triangles.
A. ΔLMN  ΔRTS
B. ΔLMN  ΔSTR
C. ΔLMN  ΔRST
D. ΔLMN  ΔTRS
5-Minute Check 1

3. Name the corresponding congruent angles for the congruent triangles.
A.  L  R, N  T, M  S
B. L  R, M  S, N  T
C. L  T, M  R, N  S
D. L  R, N  S, M  T
5-Minute Check 2

4. Name the corresponding congruent sides for the congruent triangles.
A. LM  RT, LN  RS, NM  ST
B. LM  RT, LN  LR, LM  LS
C. LM  ST, LN  RT, NM  RS
D. LM  LN, RT  RS, MN  ST
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5-Minute Check 3

5. Refer to the figure. Find the value of x.
B. 2
C. 3
D. 4
5-Minute Check 4

6. Refer to the figure. Find mA.
B. 39
C. 59
D. 63
5-Minute Check 5

7. Given that ΔABC  ΔDEF, which of the following statements is true?
A. A  E
B. C  D
C. AB  DE
D. BC  FD
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5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
Content Standards
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MP

9. You proved triangles congruent using the definition of congruence.
Use the SSS Postulate to test for triangle congruence.
Use the SAS Postulate to test for triangle congruence.
Then/Now

10. included angle
New Vocabulary

11. Postulate

12. Write a flow proof. Given: Prove:QUD ≅ ADU
Use SSS to Prove Triangles Congruent
Write a flow proof.
Given:
Prove:QUD ≅ ADU
Example 1

13. What are the given statements? QU≅ AD , QD ≅ AU
Use SSS to Prove Triangles Congruent
What are the given statements? QU≅ AD , QD ≅ AU
Why is DU ≅ DU? The Reflexive Property.
Why is ∆ QUD ≅ ∆ ADU? SSS
Use the information to write a flow proof.
Example 1

14. Use SSS to Prove Triangles Congruent
Answer: Flow Proof:
Example 1

15. A. Graph both triangles on the same coordinate plane.
SSS on the Coordinate Plane
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 using rigid motions.
C. Write a logical argument that uses coordinate geometry to support the conjecture you made in part B.
Example 2

16. SSS on the Coordinate Plane
Read the Item
You are asked to do three things in this problem. In part A, you are to graph ∆DVW and ∆LPM on the same coordinate plane. In part B, you should make a conjecture that ∆DVW ≅ ∆LPM or ∆DVW ≅ ∆LPM based on your graph. Finally, in part C, you are asked to prove your conjecture.
Example 2

17. SSS on the Coordinate PlaneB.
From the graph, there appears to be a combination of rigid motions that will map one triangle onto the other, so we can conjecture that they are congruent.
Example 2

18. SSS on the Coordinate Plane
Use the Distance Formula to show that all corresponding sides have the same measure.
Answer: DV = LP, VW = PM, and DW = LM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ∆DVW ≅ ∆LPM by SSS.
Example 2

19. Postulate

20. Entomology The wings of one type of moth
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 FEG ≅ HIG if and G is the
midpoint of both
Real-World Example 3

21. Use SAS to Prove Triangles Are Congruent
EI ≅ FH , G is the midpoint of EI and FH Write the given statements.
Why is FH ≅ HG and EG ≅ IG ? The Midpoint Theorem.
Why is  FGE ≅  HGI? Vertical Angles Theorem.
Why is ∆ FEG ≅ ∆ HIG? SAS
Use the information to write a two-column proof.
Real-World Example 3

22. Use SAS to Prove Triangles Are Congruent
Answer:
Real-World Example 3

23. Write a paragraph proof.
Use SAS or SSS in Proofs
Write a paragraph proof.
Given:
Prove: Q ≅ S
Example 4

24. RQ  TS, RQ ǁ TS, Write the given statements.
Use SAS or SSS in Proofs
RQ  TS, RQ ǁ TS, Write the given statements.
Why is  QRT ≅  STR? RQ ǁTS and alternate interior angles are congruent.
Why is RT ≅ RT ? The Reflexive Property.
Why is ∆ QRT ≅ ∆ STR? SAS
Why is  Q ≅  S? CPCTC
Use the information to write a paragraph proof.
Example 4

25. Use SAS or SSS in Proofs
Answer:
Example 4