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Lesson Menu Five-Minute Check (over Lesson 4–3) Then/Now New Vocabulary Postulate 4.1: Side-Side-Side (SSS) Congruence Example 1:Use SSS to Prove Triangles Congruent Example 2:Standard Test Example 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

Over Lesson 4–3 A.A B.B C.C D.D 5-Minute Check 1 A.ΔLMN  ΔRTS B.ΔLMN  ΔSTR C.ΔLMN  ΔRST D.ΔLMN  ΔTRS Write a congruence statement for the triangles.

Over Lesson 4–3 A.A B.B C.C D.D 5-Minute Check 2 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 Name the corresponding congruent angles for the congruent triangles.

Over Lesson 4–3 A.A B.B C.C D.D 5-Minute Check 3 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 ___

Over Lesson 4–3 A.A B.B C.C D.D 5-Minute Check 4 A.1 B.2 C.3 D.4 Refer to the figure. Find x.

Over Lesson 4–3 A.A B.B C.C D.D 5-Minute Check 5 A.30 B.39 C.59 D.63 Refer to the figure. Find m  A.

Over Lesson 4–3 A.A B.B C.C D.D 5-Minute Check 6 Given that ΔABC  ΔDEF, which of the following statements is true? A.  A   E B.  C   D C.AB  DE D.BC  FD ___

Then/Now You proved triangles congruent using the definition of congruence. (Lesson 4–3) Use the SSS Postulate to test for triangle congruence. Use the SAS Postulate to test for triangle congruence.

Vocabulary included angle

Concept 1

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

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

A.A B.B C.C D.D Example 1 CYP Which information is missing from the flowproof? Given:AC  AB D is the midpoint of BC. Prove:ΔADC  ΔADB ___ A.AC  AC B.AB  AB C.AD  AD D.CB  BC ___

Example 2A 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 2B 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 2C 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

Example 2 ANS Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔWDV  ΔMLP by SSS.

1.A 2.B 3.C Example 2A A.yes B.no C.cannot be determined Determine whether ΔABC  ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).

Concept 2

Example 3 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  HF, and G is the midpoint of both EI and HF.

Example 3 Use SAS to Prove Triangles are Congruent 3. Vertical Angles Theorem 3.  FGE   HGI 2. Midpoint Theorem2. Prove:ΔFEG  ΔHIG 4. SAS 4. ΔFEG  ΔHIG Given:EI  HF; G is the midpoint of both EI and HF. 1. Given 1.EI  HF; G is the midpoint of EI; G is the midpoint of HF. Proof: ReasonsStatements

A.A B.B C.C D.D Example 3 A.ReflexiveB. Symmetric C.TransitiveD. Substitution 3. SSS 3. ΔABG ΔCGB 2. _________ 2. ? Property 1. Reasons Proof: Statements 1. Given

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

Example 4 Use SAS or SSS in Proofs Answer:

A.A B.B C.C D.D Example 4 Choose the correct reason to complete the following flow proof. A.Segment Addition Postulate B.Symmetric Property C.Midpoint Theorem D.Substitution

End of the Lesson