Unit 2 Part 4 Proving Triangles Congruent

Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then they are congruent by ASA. Included means between

Example of ASA A F E D C B The side is between the angles.

Angle - Angle - Side Postulate If two consecutive angles and a side of a triangle are congruent to two consecutive angles and a side of another triangle, then the triangles are congruent by AAS. Consecutive means one after another. Note: the side is NOT between the angles

Example of AAS F E D C B A The side is not between the angles.

Recall Reflexive Property : such as segment AB is congruent segment AB Vertical Angles are congruent such as angle G is congruent to angle H B A D C GH

A S A

A A S

Hypotenuse-Leg Theorem (HL Theorem) If the hypotenuse and leg of a right triangle is congruent to the hypotenuse and leg of another right triangle then they are congruent.

R H L

CPCTC Corresponding Parts of Congruent Triangles are Congruent. Once you prove two triangles congruent, then all of their corresponding parts are congruent.

SSS  Side – Side – Side SAS  Side – Angle – Side AAS  Angle – Angle – Side ASA  Angle – Side – Angle HLT  Hypotenuse – Leg – Theorem Reflexive Property Vertical Angles CPCTC (corresponding parts of congruent triangles are congruent) What you should remember

S S A

Statement Reason