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Answers. 1. yes 2. no 3. yes 4. no 5. yes 1. m<A = 45; m<B =45; m<C=90 right isosceles 2. m<K =80; m<L = 60; m<M = 40;acute scalene 3. 120. Chapter 4. Congruent Triangles. Agenda and Objectives. Agenda Notes, practice, review 4-1 Notes, practice, review 4-2 Objectives

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  1. Answers • 1. yes 2. no 3. yes 4. no 5. yes • 1. m<A = 45; m<B =45; m<C=90 • right isosceles • 2. m<K =80; m<L = 60; m<M = 40;acute scalene • 3. 120

  2. Chapter 4 Congruent Triangles

  3. Agenda and Objectives • Agenda • Notes, practice, review 4-1 • Notes, practice, review 4-2 • Objectives • Identify congruent figures and corresponding parts • Prove that two triangles are congruent • Prove that triangles are congruent using the SSS and SAS Congruence Postulates

  4. Section 4-1 Congruent Figures • Review: • What makes angles ? same degree measurement • What makes segments ? same length

  5. Can an angle be congruent to a segment? Can a triangle be congruent to a square? What makes figures congruent?

  6. Congruent Figures • Two figures that have the same size and shape. • If figures are congruent then they have congruent angles and congruent sides or parts.

  7. Let’s Take a Look • Corresponding Angles • Corresponding Sides

  8. Labeling Congruent Figures • Congruent figures must be labeled according to their corresponding parts.

  9. Ex: Label the following congruent figures.

  10. Possible Answers Δ 1 Δ 3 Δ ABC Δ HGI Δ BCA Δ GIH Δ CAB Δ IHG Δ 1 Δ 2 Δ ABC Δ EFD Δ BCA Δ FDE Δ CBA Δ DFE Δ 2 Δ 3 Δ EFD Δ HGI Δ FDE Δ GHI Δ DEF Δ IHG

  11. Ex: Given: Δ CAT Δ DOG • Which angles are congruent to one another? • C and D • A and O • T and G • Which sides are congruent to one another? • CA and DO; AC and OD • AT and OG; TA and GO • TC and GD; CT and DG • To help solve, draw a picture!

  12. You try.. • Page 119 1-9, 12-17 • Please work independently • Answers • FI, WE; IN, EB; FN, WB • ∠ F, ∠ W; ∠ I, ∠ E; ∠ N, ∠ B • YES • NO • ∆CDO • ∠C • CO • DO • Yes because AO = OC and DO = OB

  13. Answers continued 12. R 13. ROHES 14. m ∠C • 4 • ∠ A • The leaf in the lower left hand corner is flipped over.

  14. Applications to Proofs • When the definition of congruent triangles is used in a proof we write, • Corr. parts of Δ’s are or CPCTC !!!

  15. Current Goal:Identify/label CPCT. Future Goal: Use parts to prove that figures are and vice versa.

  16. Example • The two triangles shown are congruent. Complete… • ∆STO ≅ ________ • ∠S ≅ ____ because ____. • SO ≅ ___ because ____. • Then point O is the midpoint of ____. • ∠T ≅ ___ because ___. • Then ST || RK because ____.

  17. Practice: Classwork Worksheet SKIP #3 Complete and we will go over.

  18. Closure to 4.1 • On a little piece of paper write never, sometimes or always. • An acute triangle is ____ congruent to an obtuse triangle. • A polygon is ____ congruent to itself. • A right triangle is _____ congruent to another right triangle. • If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y. • If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.

  19. Homeworkpage 120 Written Exercises #1-11 (SKIP 10) & #14

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