Aim: How to prove triangles are congruent using a 4 th shortcut: AAS.

Aim: Triangle Congruence - AAS Course: Applied Geometry

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Aim: How to prove triangles are congruent using a 4th shortcut: AAS.

What method shows these triangles to be congruent?

A.

ASA SAS

Aim: Triangle Congruence - AAS Course: Applied Geometry

Angle-Angle-Side

IV. AAS = AASA

B B’C C’

A’

If A = A', C = C', BC = B’C', then ABC = A'B'C'.

If AAS AAS , then the triangles are congruent

Two triangles cannot be proved to be congruent by

AAA AAA or SSA SSA

Aim: Triangle Congruence - AAS Course: Applied Geometry

Model Problems

Is the given information sufficient to prove congruent triangles?

YES

YES

D C

A B

ED

C

A

B

E

B

F

A

D

C

NO

DA B

C

YES

Aim: Triangle Congruence - AAS Course: Applied Geometry

Model Problem

BD bisects B and A C. Explain why ADB CDB.

A C – I’m told so - Given

ABD CBD – angle bisector cuts angle into two congruent parts

ADB CDB because of AAS AAS

(A A)

(A A)

BD BD – anything is equal to itself - Reflexive Property

(S S)

B

D

A C

Aim: Triangle Congruence - AAS Course: Applied Geometry

Model Problem - CPCTC

M

R A

B P

RMP bisects AMB at M, and R P. Explain why RM PM

R P – I’m told so - Given

AM MB – bisector cuts segment into two congruent parts

RMA PMB because of AAS AAS

(A A)

(S S)

RMA PMB – Vertical angles are (A A)

RM PMRM PM – Corresponding parts of congruent triangles are congruent CPCTC

Aim: Triangle Congruence - AAS Course: Applied Geometry

Model Problem