Download Notes - Congruence in Overlapping Triangles

Geometry
Name_____________________________
Notes: Overlapping Triangles (4-7)
Date___________________
Congruence in Overlapping Triangles
Essential Understanding: Sometimes you will see pictures involving _________________ triangles. You can
sometimes use the congruent corresponding parts of one pair of triangles to prove another pair of triangles
congruent. Overlapping triangles may have a common ______________ or a common _____________. You
can make these problems easier by ___________________ the overlapping triangles.
EX 1: Identifying Common Parts
What common angle do
ACD and ECB share?
E
A
B
D
C
The common angle is  _______.
EX 2: You Try!!
What is the common side in ABD and DCA ?
What is the common side in ABD and BAC
B
C
A
D
Proofs
1. Given: ZXW  YWX ,
Z
ZWX  YXW
Statements
Y
1.
Prove: ZW  YX
W
Reasons
ZXW  YWX ,
ZWX  YXW
X
2.
2.
3.
1.
ZWX  YXW
4.
Reflexive Property
3.
4.
2. Given: CA  CE , BA  DE
Prove: BX  DX
Statements
Reasons
C
B
X
A
D
1.
CA  CE , BA  DE
1.
2.
CAE  CEA
2.
3.
E
4.
3.
Reflexive Property
4.
SAS
5.
ABE  EDA
5.
6.
BXA  DXE
6.
7.
8.
BXA 
DXE
Given
7.
8.