Download Congruent Triangles:

4-4 & 4-5
Congruent Triangles:
Postulate
Side-Side-Side (SSS) Congruence:
If three sides of one triangle are
congruent to three sides of another
triangle, then the triangles are
congruent.
Hypothesis
Side-Angle Side (SAS) Congruence:
If two sides and the included angle of
one triangle are congruent to two sides
and the included angle of another
triangle, then the triangles are
congruent.
Angle-Side-Angle (ASA) Congruence:
If two angles and the included side of
one triangle are congruent to two angles
and the included side of another triangle,
then the triangles are congruent.
Angle-Angle-Side (AAS) Congruence:
If two angles and a nonincluded side of
one triangle are congruent to the
corresponding angles and nonincluded
side of another triangle, then the
triangles are congruent.
Hypotenuse-Leg (HL) Congruence:
If the hypotenuse and a leg of a right
triangle are congruent to the hypotenuse
and a leg of another right triangle, then
the triangles are congruent.
Conclusion
∆ABC
∆FDE
∆ABC
∆EFD
∆ABC
∆DEF
∆GHJ
∆KLM
∆ABC
∆DEF
______________________________: an angle formed by two adjacent sides of a polygon
______________________________: the common side of two consecutive angles in a polygon
Ex. 1: Use SSS to explain why ∆ABC
∆DBC.
It is given that: __________________________________
By the Reflexive Property of Congruence, _______________
Therefore, ______________________________________
Ex. 2: The diagram shows part of the support structure for a tower. Use SAS to explain why
∆XYZ
∆VWZ.
It is given that _______________________________________
By the Vertical Angle Theorem, ___________________________
Therefore, __________________________________________
Ex. 3: Determine if you can use ASA to prove the triangles congruent.
A.)
_________________________________
_________________________________
B.)
_________________________________
_________________________________
_________________________________
Ex. 4: Choose which triangle congruence postulate lets you conclude that the triangles are congruent.
_________________________________
Ex. 5: Determine if you can use the HL Congruence Theorem to prove the triangles congruent.
If not, tell what else you need to know.
First ask: 1. are they right triangles?
2. are the hypotenuses the same length?
3. is one pair of legs the same length?
A.
 if all of these are yes, then use HL!
1. ___________ 2. ___________ 3. ___________
_____________________________________________
B.
1. ___________ 2. ___________ 3. ___________
_____________________________________________