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 SSA condition in triangle congruence?

Back

The SSA (Side-Side-Angle) condition does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you determine if two triangles are congruent using the SSS theorem?

Back

Measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent by SSS.

Front

How can you determine if two triangles are congruent using the SAS theorem?

Back

Measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, the triangles are congruent by SAS.

Front

How can you determine if two triangles are congruent using the ASA theorem?

Back

Measure two angles and the included side of both triangles. If the two angles and the included side are equal, the triangles are congruent by ASA.

Front

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

Back

Measure two angles and a non-included side of both triangles. If the two angles and the corresponding non-included side are equal, the triangles are congruent by AAS.