Entry Task

Prove: <E + <H

4.7 Overlapping Triangles

Learning Target: • I can identify congruent OVERLAPPING triangles

• Success Criteria: I can prove triangles congruent using overlapping parts.

D E

F

G

H

The triangles may have sides or angles in common. The best way to find the necessary parts is to :

When triangles overlap it is sometimes difficult to see the correspondingcongruent parts.

Separate and redraw DFG & EHG. Identify any shared parts.

Example #1

D E

F

G

H

SHARED

Example #2Separate and redraw ACD & BDC. Identify any shared parts.

DC

A B

SHARED

Groups• On a blank computer piece of paper, groups

are to find the measure of each angle and justify that measure.

ASSIGNMENT:

Homework: P. 268 #1-3, 6, 8-13,15

Challenge - Slide #6 (worth 1 point for each correct angle measure)

Given: CA CE, BA DEWrite a two-column proof to show that CBE CDA.

3. CA = CE, BA = DE 3. Definition of congruent segments.4. CA – BA = CE – DE 4. Subtraction Property of Equality 5. CA – BA = CB, 5. Segment Addition Postulate

CE – DE = CD6. CB = CD 6. Substitution

Using Corresponding Parts of Congruent Triangles

Plan: CBE CDA by CPCTC if CBE CDA. This congruence holds by SAS if CB CD.

Proof: Statements Reasons

1. BCE DCA 1. Reflexive Property of Congruence 2. CA CE, BA DE 2. Given

7. CB CD 7. Definition of congruence 8. CBE CDA 8. SAS 9. CBE CDA 9. CPCTC Quick Check

Separating Overlapping Triangles

Example #3GIVEN: ZXW YWX

ZWX YXW PROVE: ZW YX

STATEMENTS REASONS1. 1. 2. 2.3. 3.4. 4.

XW

Z Y

STATEMENTS REASONS1. 1. 2. 2.3. 3.4. 4.

Example #4GIVEN: CA CE

BC DC PROVE: AD BE A

B

C

DXE