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Splash Screen Slide 2 Lesson Menu Five-Minute Check (over Lesson 43) 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 Slide 3 Over Lesson 43 A.A B.B C.C D.D 5-Minute Check 1 A.LMN RTS B.LMN STR C.LMN RST D.LMN TRS Write a congruence statement for the triangles. Slide 4 Over Lesson 43 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. Slide 5 Over Lesson 43 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 ___ Slide 6 Over Lesson 43 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. Slide 7 Over Lesson 43 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. Slide 8 Over Lesson 43 A.A B.B C.C D.D 5-Minute Check 6 Given that ABC DEF, which of the following statements is true? A. A E B. C D C.AB DE D.BC FD ___ Slide 9 Then/Now You proved triangles congruent using the definition of congruence. (Lesson 43) Use the SSS Postulate to test for triangle congruence. Use the SAS Postulate to test for triangle congruence. Slide 10 Vocabulary included angle Slide 11 Concept 1 Slide 12 Example 1 Use SSS to Prove Triangles Congruent Write a 2-column proof. Prove:QUD ADU Given:QU AD, QD AU ___ Slide 13 A.A B.B C.C D.D Example 1 CYP Write a two-column proof. Given:AC AB D is the midpoint of BC. Prove:ADC ADB ___ Slide 14 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. Slide 15 Example 2B Solve the Test Item a. Slide 16 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. Slide 17 Example 2C Slide 18 Example 2 ANS Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS. Slide 19 Concept 2 Slide 20 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 FEG HIG if EI HF, and G is the midpoint of both EI and HF. Slide 21 Example 3 Use SAS to Prove Triangles are Congruent 3. 3. FGE HGI 2. Prove:FEG HIG 4. 4. FEG HIG Given:EI HF; G is the midpoint of both EI and HF. 1. 1.EI HF; G is the midpoint of EI; G is the midpoint of HF. Proof: ReasonsStatements Slide 22 A.A B.B C.C D.D Example 3 3. 3. ABG CGB 2. 1. Reasons Proof: Statements 1. Slide 23 Example 4 Use SAS or SSS in Proofs Write a 2-column proof. Prove: Q S Slide 24 A.A B.B C.C D.D Example 4 Write a 2-column proof. Slide 25 End of the Lesson