 # Proving Triangles Congruent

## Presentation on theme: "Proving Triangles Congruent"— Presentation transcript:

Proving Triangles Congruent
Chapter 4, Sections 4 and 5

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.

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 = _____

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.

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

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.

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

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.

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

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.

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

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)