Congruent Triangles (SSS & SAS)

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does SSS stand for in triangle congruence?

Back

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

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 do not match in size and measure, the triangles are not congruent.

Front

What is a congruence statement?

Back

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

Front

If two triangles have two pairs of equal sides and the included angle is not equal, are they congruent?

Back

No, they are not congruent; the SAS criterion requires the included angle to be equal.

Front

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

Back

No, at least two sides and the included angle must be equal for the triangles to be congruent.

Front

What is the significance of the included angle in SAS?

Back

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

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 has sides of lengths 5 cm, 7 cm, and 9 cm, then ΔABC ≅ ΔDEF by SSS.

Front

Provide an example of SAS congruence.

Back

If triangle XYZ has sides of lengths 6 cm and 8 cm with an included angle of 60 degrees, and triangle PQR has sides of lengths 6 cm and 8 cm with the same included angle, then ΔXYZ ≅ ΔPQR by SAS.