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 two triangles are congruent.

Front

What is the SAS Triangle Congruence Theorem?

Back

The SAS Triangle 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 two sides are equal?

Back

No, two triangles cannot be proven congruent with only two sides equal; additional information, such as an included angle, is needed.

Front

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

Back

The included angle is crucial in the SAS theorem because it ensures that the two triangles are positioned in the same way, allowing for congruence.

Front

How can you prove two triangles are congruent using SSS?

Back

To prove two triangles are congruent using SSS, you must show that all three corresponding sides of the triangles are equal in length.

Front

How can you prove two triangles are congruent using SAS?

Back

To prove two triangles are congruent using SAS, you must show that two sides and the angle between them in one triangle are equal to the corresponding two sides and angle in the other triangle.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, often written in the form of triangle names, such as triangle ABC ≅ triangle DEF.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that two triangles are identical in shape and size, while similarity means that two triangles have the same shape but may differ in size.