IXL - SSS, SAS, ASA, and AAS Theorems (Geometry practice)

Which rule explains why these triangles are congruent?

ASA

AAS

SSS

SAS

These triangles cannot be proven congruent.

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question

Which rule explains why these triangles are congruent?

ASA

AAS

SAS

SSS

These triangles cannot be proven congruent.

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

First, look for congruent sides and angles.

Notice that there are no pairs of congruent sides. Since all of the congruency theorems call for at least one pair of congruent sides, there is not enough information to prove that the triangles are congruent.

Looking for more? Try these:

Lesson: Congruence

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Work it out

Not feeling ready yet? These can help:

L.2SSS and SAS Theorems

L.4ASA and AAS Theorems

Lesson: Congruence

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