1. Proving Triangles Congruent
Chapter 4, Sections 4 and 5

2. SSS Postulate (Side-Side-Side Postulate)
If the sides of one triangle are congruent to the sides of another triangle, then the 2 triangles are congruent.

3. Example 1
Given with vertices S(0, 5), T(0, 0), and U(-2, 0), and with vertices X(4, 8), Y(4, 3), and Z(6, 3), determine if 5
ST = _____ 2
TU = _____
5.4
SU = _____ 5
XY = _____ 2
YZ = _____
5.4
XZ = _____

4. SAS Postulate (Side-Angle-Side Postulate)
If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

5. Example 2 AB=DB and BC=BF. Name a pair of congruent triangles. A D B C

6. ASA Postulate (Angle-Side-Angle Postulate)
If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

7. Example 3 What is the length of XY? _______
What is the measure of <YZX? _______
Name the two congruent triangles:
_________________
30o
42o 42
30o H Z X

8. AAS Postulate (Angle-Angle-Side Postulate)
If 2 angles and a nonincluded side of one triangle are congruent to 2 angles and the nonincluded side of another triangle, then the triangles are congruent.

9. Example 4 Name the congruent triangles: _____________V S
84o
4y-11
33o
2x+4
Name the congruent triangles: _____________
Solve for all of the variables:
x = _______
y = _______
z = _______ 40 11 7

10. HL Postulate (Hypotenuse-Leg Postulate)
2 right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the second triangle.

11. Example 5
Name the congruent triangles: L P N M K

12. List all 5 methods to determine if two triangles are congruent:
_______________________
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
Hypotenuse-Leg (HL)