SSS and SAS Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem 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 theorem 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

When can you use the SSS theorem?

Back

You can use the SSS theorem when you know the lengths of all three sides of two triangles.

Front

When can you use the SAS theorem?

Back

You can use the SAS theorem when you know the lengths of two sides and the measure of the included angle of two triangles.

Front

What is the difference between SSS and SAS?

Back

SSS requires all three sides to be known, while SAS requires two sides and the included angle.

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 significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal.

Front

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

Back

No, you cannot prove congruence with two sides and a non-included angle; you need the included angle (SAS) or all three sides (SSS).

Front

What is an example of using the SSS theorem?

Back

If Triangle A has sides of lengths 5 cm, 7 cm, and 10 cm, and Triangle B also has sides of lengths 5 cm, 7 cm, and 10 cm, then Triangle A is congruent to Triangle B by SSS.

Front

What is an example of using the SAS theorem?

Back

If Triangle A has sides of lengths 6 cm and 8 cm with an included angle of 50 degrees, and Triangle B has sides of lengths 6 cm and 8 cm with the same included angle, then Triangle A is congruent to Triangle B by SAS.