4.6 Solving with Congruent Triangles

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

If △ABC ≅ △DEF, what can we say about the corresponding sides and angles?

Back

The corresponding sides and angles of the triangles are equal: AB = DE, BC = EF, AC = DF and ∠A = ∠D, ∠B = ∠E, ∠C = ∠F.

Front

What is the definition of corresponding angles?

Back

Corresponding angles are pairs of angles that are in the same position in different triangles when the triangles are congruent.

Front

If two angles of one triangle are equal to two angles of another triangle, what can be concluded about the triangles?

Back

The triangles are congruent by the Angle-Angle (AA) criterion.

Front

What is the Angle-Side-Angle (ASA) congruence criterion?

Back

The ASA criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

If BC = 15, AB = 9, and AC = 12 in triangle △BAC, what is the length of side RQ in triangle △QPR if △BAC ≅ △QPR?

Back

RQ = 15.

Front

What is the Side-Angle-Side (SAS) congruence criterion?

Back

The SAS criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

If ∠E = 45° and ∠B = 55° in congruent triangles, what is the measure of ∠ACB?

Back

∠ACB = 80°.

Front

What is the definition of corresponding sides?

Back

Corresponding sides are sides that are in the same relative position in two different triangles that are congruent.

Front

Which statement is NOT true if △ABC ≅ △LMN?

Back

BC ≅ ML is NOT true.