Geometry A 3.4 Triangle Congruence

Front

What does congruence mean in geometry?

Back

Congruence in geometry means that two figures have the same shape and size.

Front

What are the three main criteria for triangle congruence?

Back

The three main criteria for triangle congruence are: 1. Side-Angle-Side (SAS), 2. Angle-Side-Angle (ASA), 3. Side-Side-Side (SSS).

Front

What is the SAS criterion for triangle congruence?

Back

The SAS criterion 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 triangles are congruent.

Front

What is the ASA criterion for triangle congruence?

Back

The ASA criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the SSS criterion for triangle congruence?

Back

The SSS criterion states that if all three sides of one triangle are equal to all three sides of 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 determined to be congruent with only two sides known unless the included angle is also known (SAS).

Front

What is the SSA condition in triangle congruence?

Back

The SSA condition (two sides and a non-included angle) does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

How can you determine the value of a variable in a triangle?

Back

You can determine the value of a variable in a triangle by using properties of congruence, the Pythagorean theorem, or angle relationships.

Front

What is the relationship between the angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.