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Lesson 5.2 Proving Triangles are Congruent: SSS and SAS

Lesson 5.2 Proving Triangles are Congruent: SSS and SAS. Pages 241 - 244. Side-Side-Side Congruence Postulate (SSS). If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Side – BO ≅ MA Side – OW ≅ AN Side – BW ≅ MN

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Lesson 5.2 Proving Triangles are Congruent: SSS and SAS

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  1. Lesson 5.2 Proving Triangles are Congruent: SSS and SAS Pages 241 - 244

  2. Side-Side-Side Congruence Postulate (SSS) If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Side – BO ≅ MA Side – OW ≅ AN Side – BW ≅ MN Therefore, by SSS, BOW ≅ MAN

  3. Does the diagram give enough information to show that the triangles are congruent? N P M O

  4. Side-Angle-Side Congruence Postulate (SAS) 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. Side – BO ≅ MA Angle - O ≅ A Side – OW ≅ AN Therefore, by SAS, BOW ≅ MAN

  5. Does the diagram give enough information to use the SAS Congruence Postulate? A L H R P R T S

  6. Writing Proofs A proof is a convincing argument that shows why a statement is true. A two-column proof has numbered statements and reasons that show the logical order of the argument. Each statement has a reason listed to its right.

  7. How to Write a Proof • List the given information first • Use the information from the diagram • Give a reason for every statement • Use given information, definitions, postulates, and theorems as the “Reasons” • List statements in order. • End the proof with the statement that you are trying to prove.

  8. Write a 2-Column Proof that shows JKL ≅ NML Given: JL ≅ NL and L is the midpoint of KM Prove: JKL ≅ NML Statements:Reasons: 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. J M L K N

  9. Write a 2-Column Proof that shows DRA ≅ DRG Given: DR ≅ AG and RA ≅ RG Prove: DRA ≅ DRG Statements:Reasons: 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. D R G A

  10. Fill in the missing statements and missing reasons. B Given: CB ≅ CE, AC ≅ DC Prove: BCA ≅ ECD Statements:Reasons: 1. CB ≅ CE 1. 2. 2. Given 3. BCA ≅ ECD 3. 4. BCA ≅ ECD 4. D C A E

  11. Assignment: Pages 245 – 248 #16 – 26 even, #34, #36, #40 And 5.2 Practice B Worksheet

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