Congruent Triangle Problems

Using SSS, SAS, ASA, AAS: In triangle ABC and triangle DEF, if AB = DE, BC = EF, and angle A = angle D, which congruence theorem can be used to prove the triangles congruent?

• SSS

• AAA

• ASA

• SAS

Applying triangle congruence theorems: In triangle MNO and triangle PQR, if angle M = angle P, angle N = angle Q, and angle O = angle R, which congruence theorem can be used to prove the triangles congruent?

• Angle-Angle-Side (AAS) congruence theorem

• Side-Angle-Side (SAS) congruence theorem

• Angle-Side-Angle (ASA) congruence theorem

• Side-Side-Side (SSS) congruence theorem

Applying triangle congruence theorems: In triangle ABC and triangle DEF, if AB = DE, BC = EF, and AC = DF, which congruence theorem can be used to prove the triangles congruent?

• AAA Congruence Theorem

• SAS Congruence Theorem

• AAS Congruence Theorem

• SSS Congruence Theorem

Solving problems using triangle congruence: In triangle LMN and triangle XYZ, if angle L = angle X, angle M = angle Y, and LM = XY, find the measure of angle N.

• Angle N = Angle Z

• Angle N = Angle L

• Angle N = Angle Y

• Angle N = Angle X

Solving problems using triangle congruence: In triangle PQR and triangle STU, if angle P = angle S, angle Q = angle T, and PR = SU, find the measure of angle R.

• The measure of angle R is equal to the measure of angle U.

• The measure of angle R is equal to the measure of angle S.

• The measure of angle R is equal to the measure of angle Q.

• The measure of angle R is equal to the measure of angle P.

Using SSS, SAS, ASA, AAS: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, which congruence theorem can be used to prove the triangles congruent?

• SSS

• SSA

• ASA

• AAS

What does AA similarity theorem state?

• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

• If two angles of one triangle are congruent to two sides of another triangle, then the triangles are similar.

• If two sides of one triangle are congruent to two sides of another triangle, then the triangles are similar.

• If two sides of one triangle are congruent to two angles of another triangle, then the triangles are similar.

If two angles of one triangle are congruent to two angles of another triangle, then what can be said about the two triangles?

• The two triangles are parallel.

• The two triangles are similar.

• The two triangles are congruent.

• The two triangles are perpendicular.

What are the conditions for the AA similarity theorem to be applicable?

• The triangles have equal side lengths

• The triangles have a common vertex

• The triangles are both equilateral

• Two angles of one triangle are congruent to two angles of another triangle.

Are these two triangles congruent? If so, how?

• Yes, by SAS

• Yes, by AAS

• Yes, by ASA

• Yes, they look congruent.

• No they are not congruent