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 ObjectivesAgendaNotes, practice, review 4-1Notes, practice, review 4-2

Objectives Identify congruent figures and corresponding

partsProve that two triangles are congruentProve 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

Δ 1 Δ 2 Δ ABC Δ EFD Δ BCA Δ FDEΔ CBA Δ DFE

Δ 2 Δ 3

Δ EFD Δ HGI

Δ FDE Δ GHI

Δ DEF Δ IHG

Δ 1 Δ 3

Δ ABC Δ HGI

Δ BCA Δ GIH

Δ CAB Δ IHG

Ex: Given: Δ CAT Δ DOGWhich angles are congruent to one another?

C and DA and O T and G

Which sides are congruent to one another?CA and DO; AC and ODAT and OG; TA and GOTC and GD; CT and DG

To help solve, draw a picture!

You try..Page 119 1-9, 12-17

Please work independently

Answers 1. FI, WE; IN, EB; FN, WB

2. ∠ F, ∠ W; ∠ I, ∠ E; ∠ N, ∠ B3. YES

4. NO

5. ∆CDO6. ∠C7. CO8. DO9. Yes because AO = OC and DO = OB

Answers continued

12. R

13. ROHES

14. m ∠C15.4

16.∠ A17.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

On a little piece of paper write never, sometimes or always.

1. An acute triangle is ____ congruent to an obtuse triangle.

2. A polygon is ____ congruent to itself.

3. A right triangle is _____ congruent to another right triangle.

4. If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.5. If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.

Homeworkpage 120

Written Exercises #1-11 (SKIP 10) & #14