Name: ________________________________________ Date: ___________________
Geometry Unit 4 - Section 4.7
Using Corresponding Parts of Congruent Triangles
Overlapping triangles may share a common side or angle.
Simplify the overlapping triangles by separating and redrawing the triangles.
Example 1:
Separate and redraw ∆DFG and ∆EHG. Identify their shared parts.
A shared common side or angle is congruent to itself by the Reflexive Property of
Congruence.
Example 2:
Use the following information to write a proof.
Given: ZXW  YWX,
ZWX  YXW
Prove: ZW  YX
Sometimes you can prove one pair of triangles congruent and then use their
congruent corresponding parts to prove another pair congruent.
Example 3:
Using SAS and then ASA, write the following proof.
Given: PS  RS ,
PSQ  RSQ
Prove: ∆QPT  ∆QRT
Example 4:
Separate the overlapping triangles to prove parts are congruent.
Given: CAD  EAD,
C  E
Prove: BD  FD
HW: Worksheet 4.7