Proving Triangles are Congruent

Front

State if the triangles are congruent or not. If they are, state how you know.

Back

Yes - by HL

Answer explanation

The triangles are congruent by HL (Hypotenuse-Leg) because they have a pair of equal hypotenuses and one pair of equal legs, satisfying the criteria for right triangles.

Front

State if the triangles are congruent or not. If they are, state how you know.

Back

Yes - by SAS

Answer explanation

The triangles are congruent by SAS (Side-Angle-Side) because two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of the other triangle.

Front

Are the triangles congruent?

Back

Not congruent

Answer explanation

The triangles are not congruent because there is not enough information to establish any of the congruence criteria (AAS, ASA, HL, SAS). Therefore, the correct choice is 'Not congruent'.

Front

Are the triangles congruent? If yes, how?

Back

Yes - by HL

Answer explanation

The triangles are congruent by HL (Hypotenuse-Leg) because they have a pair of equal hypotenuses and one pair of equal legs, satisfying the criteria for congruence in right triangles.

Front

Are the triangles congruent? If yes, how?

Back

Yes - by SAS

Answer explanation

The triangles are congruent by SAS (Side-Angle-Side) because two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle.

Front

Back

AZY

Answer explanation

The congruence statement requires matching corresponding vertices. Since \Delta WXY is congruent to \Delta AZY, the correct completion is AZY, ensuring the order of vertices reflects the congruence.

Front

Which triangle congruence theorem can be used to prove the triangles are congruent? SAS, SSS, ASA, HL

Back

SSS

Answer explanation

The SSS (Side-Side-Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. This is the correct choice for proving triangle congruence.

Front

Which triangle congruence theorem can be used to prove the triangles are congruent? Options: SSS, ASA, AAS, SAS

Back

SAS

Answer explanation

The SAS (Side-Angle-Side) theorem can be used to prove the triangles are congruent when two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.

Front

Which triangle congruence theorem can be used to prove the triangles are congruent? Options: AAS, SSS, SAS, SSA

Back

SAS

Answer explanation

The SAS (Side-Angle-Side) theorem can be used to prove the triangles are congruent when two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.

Front

Back

Answer explanation

According to the congruency statement, ∠F is congruent to ∠G. Therefore, ∠F = ∠G, making ∠G the correct answer.