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 HB

ADC

G H

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