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4-4

4-4. Congruent Triangles. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. FG , GH , FH ,  F ,  G ,  H. Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why?

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4-4

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  1. 4-4 Congruent Triangles Holt Geometry Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry

  2. FG, GH, FH, F, G, H Warm Up 1.Name all sides and angles of ∆FGH. 2. What is true about K and L? Why? 3.What does it mean for two segments to be congruent?  ;Third s Thm. They have the same length.

  3. Objectives Use properties of congruent triangles. Prove triangles congruent by using the definition of congruence.

  4. Vocabulary corresponding angles corresponding sides congruent polygons

  5. COPY THIS SLIDE: Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if their corresponding sides are congruent.

  6. COPY THIS SLIDE:

  7. Helpful Hint Two vertices that are the endpoints of a side are called consecutive vertices. For example, P and Q are consecutive vertices.

  8. COPY THIS SLIDE: To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS. ***In a congruence statement, the order of the vertices indicates the corresponding parts.***

  9. Helpful Hint When you write a statement such as ABCDEF, you are also stating which parts are congruent. You are stating A  D, B  E, C  F, AB  DE, BC  EF, and AC  DF

  10. Sides: PQ ST, QR  TW, PR  SW Example 1: Naming Congruent Corresponding Parts COPY THIS SLIDE: Given: ∆PQR ∆STW Identify all pairs of corresponding congruent parts. Angles: P  S, Q  T, R  W

  11. Sides: LM EF, MN  FG, NP  GH, LP  EH Check It Out! Example 1 If polygon LMNP polygon EFGH, identify all pairs of corresponding congruent parts. Angles: L  E, M  F, N  G, P  H

  12. Example 2A: Using Corresponding Parts of Congruent Triangles COPY THIS SLIDE: Given: ∆ABC ∆DBC. Find the value of x. BCA andBCD are rt. s. Def. of  lines. BCA BCD Rt. Thm. Def. of  s mBCA = mBCD Substitute values for mBCA and mBCD. (2x – 16)° = 90° Add 16 to both sides. 2x = 106 x = 53 Divide both sides by 2.

  13. Example 2B: Using Corresponding Parts of Congruent Triangles COPY THIS SLIDE: Given: ∆ABC ∆DBC. Find mDBC. ∆ Sum Thm. mABC + mBCA + mA = 180° Substitute values for mBCA and mA. mABC + 90 + 49.3 = 180 Simplify. mABC + 139.3 = 180 Subtract 139.3 from both sides. mABC = 40.7 DBC  ABC Corr. s of  ∆s are  . mDBC = mABC Def. of  s. mDBC  40.7° Trans. Prop. of =

  14. AB  DE COPY THIS SLIDE: Check It Out! Example 2a Given: ∆ABC  ∆DEF Find the value of x. Corr. sides of  ∆s are. AB = DE Def. of  parts. Substitute values for AB and DE. 2x – 2 = 6 Add 2 to both sides. 2x = 8 x = 4 Divide both sides by 2.

  15. COPY THIS SLIDE: Check It Out! Example 2b Given: ∆ABC  ∆DEF Find mF. ∆ Sum Thm. mEFD + mDEF + mFDE = 180° ABC  DEF Corr. s of  ∆are . mABC = mDEF Def. of  s. mDEF = 53° Transitive Prop. of =. Substitute values for mDEF and mFDE. mEFD + 53 + 90 = 180 mF + 143 = 180 Simplify. mF = 37° Subtract 143 from both sides.

  16. Classwork/Homework • 4.4 #1-10all, 13-17odd

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