Triangle Proofs

Front

What is the definition of an isosceles triangle?

Back

A triangle with at least two congruent sides and the angles opposite those sides are also congruent.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side; it is a criterion for triangle congruence that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side; it is a criterion for triangle congruence that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the significance of congruent angles in triangle proofs?

Back

Congruent angles can help establish relationships between triangles and are often used to prove triangle congruence.

Front

What is the purpose of a proof in geometry?

Back

To provide a logical argument that demonstrates the truth of a geometric statement or theorem.

Front

What is the relationship between the angles in an isosceles triangle?

Back

The angles opposite the congruent sides are equal.

Front

What is the first step in proving two triangles are congruent?

Back

Identify and establish the congruence of at least one pair of corresponding sides or angles.

Front

How can you determine if two triangles are congruent using the AAS criterion?

Back

Show that two angles and the non-included side of one triangle are congruent to the corresponding two angles and the non-included side of another triangle.

Front

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

Back

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

Front

What is a congruence statement?

Back

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