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Warm Up 1. Name all sides and angles of ∆ FGH .

FG , GH , FH ,  F ,  G ,  H. Warm Up 1. Name all sides and angles of ∆ FGH . 2. What does it mean for two segments to be congruent?. They have the same length. 4.1 Congruent Figures. Target: SWBAT recognize congruent figures and their corresponding parts.

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Warm Up 1. Name all sides and angles of ∆ FGH .

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  1. FG, GH, FH, F, G, H Warm Up 1.Name all sides and angles of ∆FGH. 2.What does it mean for two segments to be congruent? They have the same length.

  2. 4.1 Congruent Figures Target: SWBAT recognize congruent figures and their corresponding parts.

  3. Sides: PQ ST, QR  TW, PR  SW Example 1: Naming Congruent Corresponding Parts Given: ∆PQR ∆STW (order matters!!) Sometimes a picture can help … Identify all pairs of corresponding congruent parts. Angles: P  S, Q  T, R  W R S W T P Q

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

  5. AB  DE 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 2x = 8 Add 2 to both sides. x = 4 Divide both sides by 2.

  6. Check It Out! Example 2b Given: ∆ABC  ∆DEF Find mF. C F Corr. s of  ∆are . ∆ Sum Thm. mA+ mB+ mC= 180° 90+ 53 + m C = 180° Substitute known values and solve for mC 143 + mC = 180° mC= 37° mF= 37°

  7. Assignment #32 – Pages 222-224 Foundation: (11-29 odd, 32) Core: (35-39 odd, 40, 41) Challenge: (47)

  8. Check It Out! Example 3 Given:ADbisectsBE. BEbisectsAD. ABDE, A D Prove:∆ABC  ∆DEC

  9. 4.ABDE 5.ADbisectsBE, 6.BC EC, AC DC BE bisects AD 1.A D 1. Given 2.BCA  DCE 2. Vertical s are . 3.ABC DEC 3. Third s Thm. 4. Given 5. Given 6. Def. of bisector 7.∆ABC  ∆DEC 7. Def. of  ∆s

  10. RS Exit Slip 1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB. Given that polygon MNOP polygon QRST, identify the congruent corresponding part. 2. NO  ____ 3. T  ____ 4. Given: C is the midpoint of BD and AE. A  E, AB  ED Prove: ∆ABC  ∆EDC 31, 74 P

  11. Statements Reasons 1. A  E 1. Given 2. C is mdpt. of BD and AE 2. Given 3. AC EC; BC  DC 3. Def. of mdpt. 4. AB ED 4. Given 5. ACB  ECD 5. Vert. s Thm. 6. B  D 6. Third s Thm. 7. ABC  EDC 7. Def. of  ∆s

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