Proving Triangles 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 all 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 applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What does AAA mean in triangle congruence?

Back

AAA (Angle-Angle-Angle) indicates that if three angles of one triangle are equal to three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

Can two triangles be congruent if only one side is known?

Back

No, knowing only one side is not enough information to prove congruence; at least two sides and the included angle or other congruence criteria must be used.

Front

If two triangles have two sides equal and the included angle is not known, can they be proven congruent?

Back

No, without knowing the included angle, you cannot use the SAS theorem, and thus cannot prove congruence.

Front

What is the importance of proving triangles congruent in geometry?

Back

Proving triangles congruent helps establish relationships between different geometric figures, allowing for the application of various geometric properties and theorems.