Congruent Triangles (SSS & SAS)

Front

What are congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side', a criterion for triangle congruence stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for 'Side-Angle-Side', a criterion for triangle congruence stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

How can you determine if two triangles are congruent using SSS?

Back

Measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent by SSS.

Front

How can you determine if two triangles are congruent using SAS?

Back

Measure two sides and the included angle of both triangles. If the two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle, they are congruent by SAS.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates two geometric figures are congruent, typically written in the form ΔABC ≅ ΔDEF.

Front

If two triangles are not congruent, what can be said about their sides and angles?

Back

If two triangles are not congruent, at least one pair of corresponding sides or angles is not equal.

Front

Can two triangles be congruent if only one pair of sides is equal?

Back

No, two triangles cannot be congruent if only one pair of sides is equal; at least two sides and the included angle must be equal (SAS) or all three sides must be equal (SSS).

Front

What is the importance of the included angle in SAS?

Back

The included angle in SAS is crucial because it is the angle formed between the two sides being compared; it ensures that the triangles are not only similar in side lengths but also in shape.

Front

Provide an example of SSS congruence. If triangle ABC has sides of lengths 5 cm, 7 cm, and 9 cm, and triangle DEF has sides of lengths 5 cm, 7 cm, and 9 cm, are they congruent?

Back

Yes, triangle ABC and triangle DEF are congruent by SSS because all three corresponding sides are equal.