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Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why?

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. Goals of the Day!.

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Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why?

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  1. 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.

  2. Goals of the Day! Use properties of congruent triangles.

  3. Terms (Add to your definition sheet) • Congruent figures – Two figures whose corresponding sides and corresponding angles are congruent.

  4. Describing Congruent Triangles • In the diagram ΔMLK ≅ ΔJTE Complete the statements. • ∠L ≅ ________ • MK ≅ ________ • m∠M = ______° • m∠T =_______° • ML ≅ ________ • ΔETJ ≅ _______

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

  6. How to name a polygon! 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.

  7. Helpful Hint When you write a statement such as ABCDEF, you are also stating which parts are congruent.

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

  9. Warm Up • In the diagram ΔMLK ≅ ΔJTE Complete the statements. • ∠E ≅ ________ • LK ≅ ________ • m∠E= ______° • m∠T =_______° • LM ≅ ________ • ΔKML ≅ _______

  10. Naming Congruent Figures • Write the angle congruence statements • ∠A ≅ ∠C Given • ∠D ≅ ∠B Given • ∠B ≅ ∠D Given • Write the side congruence statements • AD ≅ CB Given • AB ≅ CD Given • BD ≅ BD Reflexive • Therefore ΔADB ≅ ΔCBD A C D B B D

  11. Naming Congruent Figures • Identify any figures that can be proved congruent. Explain your reasoning. For those that can be proved congruent, write a congruent statement.

  12. When two figures are not congruent. ∠M ≅ ∠O Given ∠N ≅ ∠P Given ∠Q ≅ ∠Q Reflexive Sides ??? Not Enough Information, so triangles are not congruent.

  13. Example: Using Algebra and Congruent Triangles Given: ∆ABC  ∆DEF Find the value of x. First: Redraw the triangles so they are oriented in the same positions. Mark off the congruent sides with hash marks! AB = DE Substitute values for AB and DE. 2x – 2 = 6 Add 2 to both sides. 2x = 8 x = 4 Divide both sides by 2.

  14. Find the measure of the missing angle Given: ∆ABC  ∆DEF Find mF. ∆ Sum Thm. mEFD + mDEF + mFDE = 180° mEFD + 53 + 90 = 180 Substitute values for mDEF and mFDE. mF + 143 = 180 Simplify. mF = 37° Subtract 143 from both sides.

  15. Using Algebra

  16. Try this one 

  17. RS Lesson Quiz 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  ____ 31, 74 P

  18. Assignment • P 234 3-10, 13-18, 23-25

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