Download 4.5-4.7 Notes - Garnet Valley School

Geometry B
Date: _______________
4.5-4.7 Triangle Congruence Theorems
Objective: To apply triangle congruence theorems to solve problems
Recall: Congruent Triangles have ___ pairs of congruent angles and ____ pairs of congruent sides.
If we need to prove two triangles are congruent, it seems like a lot of work to have to prove there are 3
pairs of congruent angles and 3 pairs of congruent sides. Luckily, there are 5 shortcuts to proving two
triangles are congruent. The shortcuts are listed below:
SSS: _________ – _________ – _________
If ___________________________ are congruent, then the triangles must be congruent.
SAS: _________ – _________ – _________
If two sides and their ________________________ are congruent, then the triangles must be congruent.
*The included angle is the angle BETWEEN the two sides.
Ex. 1: Using SSS and SAS to Prove Triangle Congruence
Determine whether there is enough information to prove that the triangles are congruent. If yes, state the
reason why you know they are congruent.
a.
b.
c.
ASA: _________ – _________ – _________
If two angles and their _________________________ are congruent, then the triangles must be
congruent.
AAS: _________ – _________ – _________
If two angles and their _________________________ are congruent, then the triangles must be
congruent.
To prove that two right triangles are __________________, we only need to know that the
_______________________ and one of the ______________ are congruent.
**HL = ___________________ – ____________
Right Triangles Only!
If two right triangles have one ________ that is congruent and their __________________ are
congruent, then the triangles must be congruent.
DO NOT USE: ______________ and ______________. They cannot guarantee triangle congruence.
Ex. 2: Proving Triangle Congruence
Determine whether there is enough information to tell that the triangles are congruent.
If yes, state the reason why you know they are congruent.
HW: 4.5-4.7 Worksheet