SSS and SAS Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the SSS Congruence Theorem?

Back

The SSS Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS Congruence Theorem?

Back

The SAS Congruence Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

Can two triangles be congruent if only one side is known?

Back

No, you need at least two sides and the included angle (SAS) or all three sides (SSS) to prove congruence.

Front

What is the importance of the included angle in SAS?

Back

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

Front

If two triangles have two equal sides and a non-included angle, are they congruent?

Back

No, having two equal sides and a non-included angle does not guarantee triangle congruence.

Front

What is an example of using SSS to prove 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 Triangle ABC is congruent to Triangle DEF by SSS.

Front

What is an example of using SAS to prove congruence?

Back

If Triangle XYZ has sides of lengths 6 cm, 8 cm, and an included angle of 60 degrees, and Triangle PQR has sides of lengths 6 cm, 8 cm, and an included angle of 60 degrees, then Triangle XYZ is congruent to Triangle PQR by SAS.

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.