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* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 Identify congruent figures and corresponding parts Prove that two triangles are congruent Prove that triangles are congruent using the SSS and SAS Congruence Postulates Section 4-1 Congruent Figures Review: What makes angles ? same degree measurement What makes segments same length ? Can an angle be congruent to a segment? Can a triangle be congruent to a square? What makes figures congruent? 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. Let’s Take a Look Corresponding Angles Corresponding Sides Labeling Congruent Figures Congruent figures must be labeled according to their corresponding parts. Ex: Label the following congruent figures. Possible Answers Δ1 Δ2 Δ ABC Δ EFD Δ BCA Δ FDE Δ CBA Δ DFE Δ2 Δ EFD Δ FDE Δ DEF Δ1 Δ ABC Δ BCA Δ CAB Δ3 Δ HGI Δ GHI Δ IHG Δ3 Δ HGI Δ GIH Δ IHG 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! You try.. Page 119 1-9, 12-17 Please work independently Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 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 Answers continued 12. R 13. ROHES 14. m ∠C 15. 4 16. ∠ A 17. The leaf in the lower left hand corner is flipped over. Applications to Proofs When the definition of congruent triangles is used in a proof we write, Corr. parts of Δ’s are or CPCTC !!! Current Goal:Identify/label CPCT. Future Goal: Use parts to prove that figures are and vice versa. 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 ____. Practice: Classwork Worksheet SKIP #3 Complete and we will go over. Closure to 4.1 1. 2. 3. 4. 5. 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. Homework page 120 Written Exercises #1-11 (SKIP 10) & #14