Triangle Congruence - SAS & SSS

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 condition for using the SSS theorem?

Back

The SSS theorem can be used when all three sides of two triangles are known and can be compared.

Front

What is the condition for using the SAS theorem?

Back

The SAS theorem can be used when two sides and the angle between them in one triangle are known and can be compared to another triangle.

Front

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

Back

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

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.

Front

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

Back

No, this situation does not satisfy the conditions of SAS or SSS, and thus cannot be used to prove congruence.

Front

What is the significance of the included angle in the SAS theorem?

Back

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

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 60 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.