IXL - SSS and SAS Theorems (Geometry practice)

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

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question

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

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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 SAS Theorem states that two triangles are congruent if and only if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Find the two triangles with two pairs of congruent sides and congruent included angles.

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Side

∠

≅

Angle

∠

Angle

≅

Side

Two sides and the included angle of

△

are congruent to two sides and the included angle of

△

so these triangles are congruent by the SAS Theorem.

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

∠

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∠

corresponds to

Also, since the side opposite

corresponds to the side opposite

corresponds to

Similarly,

corresponds to

So,

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Looking for more? Try these:

Lesson: Congruence

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K.3Identify congruent figures

Lesson: Congruence

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