Triangle Proof Theorems

Front

What is the definition of congruent triangles?

Back

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

Front

What does the Side-Angle-Side (SAS) congruence theorem state?

Back

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 Angle-Angle-Side (AAS) congruence theorem?

Back

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

Explain the Angle-Side-Angle (ASA) congruence theorem.

Back

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 Side-Side-Side (SSS) congruence theorem?

Back

If all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What does SSA stand for in triangle congruence?

Back

Side-Side-Angle; it does not guarantee triangle congruence.

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is the angle formed between two sides of a triangle; it is crucial for the SAS and ASA theorems.

Front

Can two triangles be congruent if only two sides are known?

Back

Not necessarily; additional information about angles or the third side is needed to confirm congruence.

Front

What additional information is required for two triangles to be congruent by SAS?

Back

The included angle between the two known sides must be equal.

Front

What is the definition of the term 'corresponding parts' in triangle congruence?

Back

Corresponding parts are the sides and angles of triangles that are in the same relative position.