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**Proving Triangles Congruent**

Chapter 4, Sections 4 and 5

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**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.

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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 = _____

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**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.

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

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**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.

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**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

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**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.

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**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

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**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.

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

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**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)

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