jessie
Uploaded by
23 SLIDES
332 VIEWS
230LIKES

Congruent Triangles: Understanding and Applications

DESCRIPTION

Learn to identify and prove congruent triangles using SSS and SAS postulates. Understand corresponding parts, labels, and angle measurements in this detailed lesson. Practice worksheets included.

1 / 23

Download Presentation

Congruent Triangles: Understanding and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related