IXL - ASA and AAS Theorems (Geometry practice)

Which two triangles are congruent by the ASA Theorem? Complete the congruence statement.

△

≅

△

ref_doc_title.

Learn with an example

question

Which two triangles are congruent by the AAS Theorem? Complete the congruence statement.

△

≅

△

key idea

Two triangles are congruent if they have the same size and shape. Here are the four common ways to prove that two triangles are congruent:


SSS (side-side-side) All three corresponding sides are congruent.	SAS (side-angle-side) Two sides and the angle between them are congruent.

ASA (angle-side-angle) Two angles and the side between them are congruent.	AAS (angle-angle-side) Two angles and a non-included side are congruent.

solution

The AAS Theorem states that two triangles are congruent if and only if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of the other triangle.

Find the two triangles with two pairs of congruent angles and a pair of congruent corresponding non-included sides.

∠

≅

Angle

∠

Angle

∠

≅

Angle

∠

Angle

≅

Side

Two angles and a non-included side of

△

are congruent to two angles and the corresponding non-included side of

△

so these triangles are congruent by the AAS Theorem.

To write the congruence statement, match the corresponding vertices. Since

∠

≅

∠

and

∠

≅

∠

corresponds to

and

corresponds to

Therefore,

corresponds to

and

△

≅

△

Looking for more? Try these:

Lesson: Congruence

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

K.3Identify congruent figures

Lesson: Congruence

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!