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 not congruent?

Back

If the corresponding sides and angles of two triangles do not match, the triangles are not congruent.

Front

Provide an example of SSS congruence.

Back

If triangle ABC has sides of lengths 5 cm, 7 cm, and 9 cm, and triangle DEF also has sides of lengths 5 cm, 7 cm, and 9 cm, then triangle ABC is congruent to triangle DEF by SSS.

Front

Provide an example of SAS congruence.

Back

If triangle XYZ has sides XY = 6 cm, XZ = 8 cm, and angle Y = 60 degrees, and triangle PQR has sides PQ = 6 cm, PR = 8 cm, and angle Q = 60 degrees, then triangle XYZ is congruent to triangle PQR by SAS.

Front

What is a congruence statement?

Back

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

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence.

Front

Can two triangles be congruent if only two sides are equal?

Back

No, two triangles cannot be determined to be congruent with only two sides equal unless the included angle is also known (SAS).

Front

What is the relationship between corresponding angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal.