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Entry Task
4.7 Overlapping Triangles
G
H
F
D
Learning Target:
•I can identify congruent OVERLAPPING
triangles
•Success Criteria: I can prove triangles
congruent using overlapping parts.
E
When triangles overlap it is sometimes
difficult to see the corresponding
congruent parts.
The triangles may have sides or angles
in common. The best way to find
the necessary parts is to :
Example #1
Separate and redraw DFG & EHG.
Identify any shared parts.
G
H
F
D
E
SHARED
Example #2
Separate and redraw ACD & BDC.
Identify any shared parts.
A
B
C
D
SHARED
Example #3
GIVEN: ZXW YWX Z
ZWX YXW
PROVE:
ZW YX W
STATEMENTS
1.
1.
2.
3.
4.
2.
3.
4.
Y
X
REASONS
Using Corresponding Parts of Congruent Triangles
Separating Overlapping Triangles
Given: CA CE, BA DE
Write a two-column proof to show that CBE
Plan: CBE CDA by CPCTC if CBE
congruence holds by SAS if CB CD.
Reasons
Proof: Statements
1. BCE DCA
2. CA CE, BA DE
3. CA = CE, BA = DE
4. CA – BA = CE – DE
5. CA – BA = CB,
CE – DE = CD
6. CB = CD
7. CB CD
8. CBE
CDA
9. CBE CDA
CDA.
CDA. This
1. Reflexive Property of Congruence
2. Given
3. Definition of congruent segments.
4. Subtraction Property of Equality
5. Segment Addition Postulate
6. Substitution
7. Definition of congruence
8. SAS
9. CPCTC
Quick Check
Example #4
C
GIVEN: CA CE
BC DC B X
PROVE: AD BE A
STATEMENTS
1.
1.
2.
3.
4.
2.
3.
4.
D
E
REASONS
ASSIGNMENT:
Homework: P. 268 #1-13,15,16, 20
Challenge - #20
Groups
• On a blank computer piece of paper, groups
are to find the measure of each angle and
justify that measure.