Five-Minute Check (over Lesson 4 3) CCSS Then/Now New Vocabulary Postulate 4.1: Side-Side-Side (SSS) Congruence Example 1: Use SSS to Prove Triangles
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2 Five-Minute Check (over Lesson 4 3) CCSS 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: 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
3 Over Lesson 4 3 Write a congruence statement for the triangles. A. ΔLMN ΔRTS B. ΔLMN ΔSTR C. ΔLMN ΔRST D. ΔLMN ΔTRS
4 Over Lesson 4 3 Write a congruence statement for the triangles. A. ΔLMN ΔRTS B. ΔLMN ΔSTR C. ΔLMN ΔRST D. ΔLMN ΔTRS
5 Over Lesson 4 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
6 Over Lesson 4 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
7 Over Lesson 4 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
8 Over Lesson 4 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
9 Over Lesson 4 3 Refer to the figure. Find x. A. 1 B. 2 C. 3 D. 4
10 Over Lesson 4 3 Refer to the figure. Find x. A. 1 B. 2 C. 3 D. 4
11 Over Lesson 4 3 Refer to the figure. Find m A. A. 30 B. 39 C. 59 D. 63
12 Over Lesson 4 3 Refer to the figure. Find m A. A. 30 B. 39 C. 59 D. 63
13 Over Lesson 4 3 Given that ΔABC ΔDEF, which of the following statements is true? A. A E B. C D C. AB DE D. BC FD
14 Over Lesson 4 3 Given that ΔABC ΔDEF, which of the following statements is true? A. A E B. C D C. AB DE D. BC FD
15 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.
16 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.
17 included angle
18
19 Write a flow proof. Use SSS to Prove Triangles Congruent Given: Prove: QU AD, QD AU ΔQUD ΔADU
20 Answer: Use SSS to Prove Triangles Congruent
21 Answer: Flow Proof: Use SSS to Prove Triangles Congruent
22 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
23 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
24 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.
25 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. SSS on the Coordinate Plane
26 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.
27 SSS on the Coordinate Plane
28 Answer: SSS on the Coordinate Plane
29 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.
30 Determine whether ΔABC ΔDEF for A( 5, 5), B(0, 3), C( 4, 1), D(6, 3), E(1, 1), and F(5, 1). A. yes B. no C. cannot be determined
31 Determine whether ΔABC ΔDEF for A( 5, 5), B(0, 3), C( 4, 1), D(6, 3), E(1, 1), and F(5, 1). A. yes B. no C. cannot be determined
32
33 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.
34 Use SAS to Prove Triangles are Congruent Given: EI FH; G is the midpoint of both EI and FH. Prove: ΔFEG ΔHIG Proof: Statements 1. EI FH; G is the midpoint of EI; G is the midpoint of FH. Reasons 1. Given FGE HGI 4. ΔFEG ΔHIG 2. Midpoint Theorem 3. Vertical Angles Theorem 4. SAS
35 The two-column proof is shown to prove that ΔABG ΔCGB if ABG CGB and AB CG. Choose the best reason to fill in the blank. Proof: Statements Reasons 1. Given 2.? Property 3. ΔABG ΔCGB 3. SSS A. Reflexive B. Symmetric C. Transitive D. Substitution
36 The two-column proof is shown to prove that ΔABG ΔCGB if ABG CGB and AB CG. Choose the best reason to fill in the blank. Proof: Statements Reasons 1. Given 2.? Property 3. ΔABG ΔCGB 3. SSS A. Reflexive B. Symmetric C. Transitive D. Substitution
37 Use SAS or SSS in Proofs Write a paragraph proof. Prove: Q S
38 Answer: Use SAS or SSS in Proofs
39 Answer: Use SAS or SSS in Proofs
40 Choose the correct reason to complete the following flow proof. A. Segment Addition Postulate B. Symmetric Property C. Midpoint Theorem D. Substitution
41 Choose the correct reason to complete the following flow proof. A. Segment Addition Postulate B. Symmetric Property C. Midpoint Theorem D. Substitution
42
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