Triangle Proofs

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, triangle ABC is congruent to triangle ABC.

Front

What does SAS (Side-Angle-Side) mean in triangle congruence?

Back

SAS 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 is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (or vertical) angles are congruent.

Front

What is the SSS (Side-Side-Side) Congruence Theorem?

Back

The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Congruence Theorem states that 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 HL (Hypotenuse-Leg) Congruence Theorem?

Back

The HL Congruence Theorem applies to right triangles and states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the Transitive Property in geometry?

Back

The Transitive Property states that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third quantity.

Front

What are congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

What is the purpose of triangle proofs?

Back

Triangle proofs are used to demonstrate the congruence of triangles using various properties and theorems, providing a logical argument for why two triangles are the same.

Front

What is the significance of the Side-Angle-Side (SAS) criterion?

Back

The SAS criterion is significant because it provides a method to prove triangle congruence using only two sides and the angle between them.