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Do Now 1 . ∆ QRS  ∆ LMN . Name all pairs of congruent corresponding parts.

QR  LM , RS  MN , QS  LN ,  Q   L ,  R   M ,  S   N. Do Now 1 . ∆ QRS  ∆ LMN . Name all pairs of congruent corresponding parts. 2. Find the equation of the line through the points (3, 7) and (5, 1). y - 1 = -3(x - 5) or y - 7 = -3(x - 3) o r y = -3x + 16.

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Do Now 1 . ∆ QRS  ∆ LMN . Name all pairs of congruent corresponding parts.

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  1. QR  LM, RS  MN, QS  LN, Q  L, R  M, S  N • Do Now • 1.∆QRS  ∆LMN. Name all pairs of congruent corresponding parts. • 2. Find the equation of the line through the points (3, 7) and (5, 1) y - 1 = -3(x - 5) or y - 7 = -3(x - 3) or y = -3x + 16

  2. 4.2 Triangle Congruence TARGET: SWBAT Prove triangles congruent by using SSS and SAS.

  3. It is given that AC DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS. Example 1: Using SSS to Prove Triangle Congruence Use SSS to explain why ∆ABC  ∆DBC.

  4. It is given that AB CD and BC  DA. By the Reflexive Property of Congruence, AC  CA. So ∆ABC  ∆CDAby SSS. Example 2 – More with SSS Write a Congruence Statement for the following triangles.

  5. An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between sides AB and BC.

  6. It can also be shown that only two pairs of congruent corresponding sides are needed to prove the congruence of two triangles if the included angles are also congruent. This is Postulate 4-2 (SAS)

  7. Caution The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides.

  8. It is given that XZ VZ and that YZ  WZ. By the Vertical s Theorem. XZY  VZW. Therefore ∆XYZ  ∆VWZ by SAS. Example 3: Engineering Application The diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ  ∆VWZ.

  9. It is given that BA BD and ABC  DBC. By the Reflexive Property of congruence, BC  BC. So ∆ABC  ∆DBCby SAS. Example 4 – More with SAS Write a Congruence Statement for the following triangles.

  10. 3.BC || AD 1.BC  AD 2.BD BD Example 5: Proving Triangles Congruent Given: BC║ AD, BC AD Prove: ∆ADB ∆CBD Statements Reasons 1.Given 2.Reflex. Prop. of  3.Given 4.Alt. Int. s Thm. 4.CBD  ADB 5.∆ADB ∆CBD 5.Side-Angle-Side

  11. 2.QP bisects RQS 1. QR  QS 4. QP  QP Example 6 – More with SAS Given: QP bisects RQS. QR QS Prove: ∆RQP  ∆SQP Statements Reasons 1. Given 2. Given 3.RQP  SQP 3. Def. of bisector 4. Reflex. Prop. of  5.∆RQP  ∆SQP 5.Side-Angle-Side

  12. Assignment #33 - Pages 230-233 Foundation: 1-3, 8, 9, 11-14 Core: 16, 19, 24-26

  13. Lesson Quiz: Part I Which postulate, if any, can be used to prove the triangles congruent? 2. 1. none SSS

  14. Statements Reasons 1.PN bisects MO 2.MN  ON 3.PN PN 4.PN MO 5.PNM and PNO are rt. s 6.PNM  PNO 7.∆MNP  ∆ONP 1. Given 2. Def. of bisect 3. Reflex. Prop. of  4. Given 5. Def. of  6. Rt.   Thm. 7. SAS Steps 2, 6, 3 Lesson Quiz: Part II 3. Given: PN bisects MO,PN  MO Prove: ∆MNP  ∆ONP

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