AAS examples

By: Ana Cristina Andrade

A

DC

E

VVGiven: segment AD is parallel to

segment BC. Segment AD is congruent to segment CBProof: Triangle AED congruent to triangle CEB

Statement Reasons

Segment AD is parallel to segment BC.

Given

Angle DAE is congruent to angle BEC

Alternate interior angle theorem

Angle AED is congruent to angle BCE

Vertical angles theorem

AD is congruent to CD Given

Triangle AED is congruent to triangle CEB

AAS

Example # 1:B

Example # 2:A

B

DC

>

>

Given: Angle B and angle D are right angles. Segment AB is parallel to segment DC.Proof: Triangle ADC is congruent to triangle BAC.

Statement Reason

Angle B and angle D are right angles. Segment AB is parallel to segment DC

given

AC is congruent to AC Reflexive property

Angle DAC is congruent to angle ACB

Alternate interior angles theorem

Angle ADC is congruent to angle ABC

Right angle theorem

Triangle ADC is congruent to triangle BAC

AAS

Example # 3:

A B

C

DE

F

Given: Segment AB is congruent to segment DE. Angle C is congruent to angle F.Proof: Triangle ABC is congruent to triangle DEF.

Statement reason

Segment AB is congruent to segment DE. Angle C is congruent to angle F. Angle A & angle D are right angles

Given

Angle A is congruent to angle D

Right angles theorem

Triangle ABE is congruent to triangle DCE.

AAS