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 two 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 two triangles are congruent.

Front

What is the SSS Triangle Congruence Theorem?

Back

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

Front

What is the SAS Triangle Congruence Theorem?

Back

The SAS Triangle Congruence Theorem states that if two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the triangles are congruent.

Front

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

Back

No, knowing only one side is not enough to prove triangle congruence. You need at least two sides and the included angle (SAS) or all three sides (SSS).

Front

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

Back

No, two triangles with two equal sides and a non-included angle are not necessarily congruent. This is known as the SSA condition, which does not guarantee congruence.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important because it allows us to determine that two triangles are identical in shape and size, which is fundamental in proving other geometric properties.

Front

What is an example of using the SSS theorem?

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

What is an example of using the SAS theorem?

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