Proving Triangles are Congruent

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the SSS Congruence Theorem?

Back

The SSS (Side-Side-Side) 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 (Side-Angle-Side) 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 triangles are congruent.

Front

What is the ASA Congruence Theorem?

Back

The ASA (Angle-Side-Angle) Congruence Theorem 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 AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the HL Congruence Theorem?

Back

The HL (Hypotenuse-Leg) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

Which triangle congruence theorem is NOT a valid shortcut?

Back

SSA (Side-Side-Angle) is NOT a valid shortcut to prove triangles congruent.

Front

What is the Reflexive Property in triangle congruence?

Back

The Reflexive Property states that a triangle is congruent to itself, meaning any triangle can be used in congruence statements with itself.

Front

How can you determine if two triangles are congruent using measurements?

Back

By measuring the lengths of corresponding sides and the sizes of corresponding angles, you can apply the congruence theorems (SSS, SAS, ASA, AAS, HL) to determine congruence.

Front

What is the significance of corresponding parts in triangle congruence?

Back

Corresponding parts (sides and angles) must be equal for two triangles to be considered congruent.