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 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 triangles are congruent.

Front

What is the SAS Congruence Theorem?

Back

The SAS 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 two sides are known?

Back

No, two triangles cannot be proven congruent with only two sides known unless the included angle is also known (SAS).

Front

What is the importance of the included angle in SAS?

Back

The included angle is crucial in SAS because it is the angle formed between the two sides being compared, which helps establish congruence.

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 cannot be proven congruent; this is known as the SSA condition.

Front

What is the difference between SSS and SAS?

Back

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

Front

What is an example of SSS in practice?

Back

If Triangle A has sides of lengths 5 cm, 7 cm, and 9 cm, and Triangle B also has sides of lengths 5 cm, 7 cm, and 9 cm, then Triangle A is congruent to Triangle B by SSS.

Front

What is an example of SAS in practice?

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.