Identifying and Applying Triangle Congruence Criteria

Two triangles, ABC and DEF, are such that AB = DE, AC = DF, and angle A = angle D. Are triangles ABC and DEF congruent? If so, which triangle congruence criterion applies?

• Yes, triangles ABC and DEF are congruent by AAS criterion.

• Yes, triangles ABC and DEF are congruent by SSS criterion.

• Yes, triangles ABC and DEF are congruent by ASA criterion.

• No, triangles ABC and DEF are not congruent because they have different angles.

In a park, two triangular flower beds, XYZ and PQR, have sides XY = PQ, YZ = QR, and angle Y = angle Q. Determine if the flower beds are congruent and state the criterion used.

• No, the flower beds are congruent by the AAS criterion.

• Yes, the flower beds are congruent by the ASA criterion.

• Yes, the flower beds are congruent by the SAS criterion.

• No, the flower beds are not congruent by the SSS criterion.

A bridge is designed with two triangular supports, GHI and JKL, where GH = JK, HI = KL, and angle H = angle K. Are the supports congruent? Explain your reasoning using a triangle congruence criterion.

• Yes, the supports are congruent but only if they are the same color.

• No, the supports are congruent only if they are the same size.

• Yes, the supports are congruent.

• No, the supports are not congruent because they have different angles.

During a construction project, two triangular sections of a roof, MNO and PQR, are found to have sides MN = PQ, NO = QR, and angle N = angle R. Are these sections congruent? Which criterion confirms this?

• Yes, the sections are congruent by the AAS criterion.

• No, the sections are congruent by the ASA criterion.

• No, the sections are not congruent by the SSS criterion.

• Yes, the sections are congruent by the SAS criterion.

A triangular garden, ABC, has a side length of 10 meters, and another triangular garden, DEF, has a side length of 10 meters as well. If angle A = angle D, can you conclude that the gardens are congruent? Why or why not?

• No, the gardens are not necessarily congruent.

• Yes, the gardens are congruent because they have equal side lengths.

• The gardens are congruent because they have the same area.

• Yes, the gardens are congruent since they have one angle equal.

In a school project, students create two triangular models, JKL and MNO, where JK = MN, KL = NO, and angle K = angle O. Are the models congruent? Identify the triangle congruence criterion that applies.

• Yes, the models are congruent by the ASA criterion.

• No, the models are congruent by the SSS criterion.

• Yes, the models are not congruent by the AAS criterion.

• No, the models are congruent by the SAS criterion.

Two triangular pieces of art, PQR and STU, are such that PQ = ST, QR = TU, and angle R = angle T. Are the pieces congruent? Justify your answer with the appropriate criterion.

• No, the pieces are not congruent because they have different angles.

• Yes, but only if the sides are equal in length.

• No, the pieces are congruent only if they are similar.

• Yes, the pieces are congruent.

A triangular plot of land, ABC, has a height of 5 meters and a base of 12 meters. Another plot, DEF, has the same height and base. Are the plots congruent? Explain your reasoning using triangle congruence criteria.

• Yes, the plots are congruent but only if they are rotated.

• No, the plots are not congruent as they have different base lengths.

• No, the plots are not congruent because they have different heights.

• Yes, the plots are congruent.

In a design competition, two triangular logos, XYZ and ABC, have sides XY = AB, YZ = BC, and angle Z = angle C. Are the logos congruent? State the triangle congruence criterion that applies.

• Yes, the logos are congruent by the SAS criterion.

• Yes, the logos are congruent by the SSS criterion.

• No, the logos are not congruent by the AAS criterion.

• No, the logos are congruent by the ASA criterion.

Two triangular sails, DEF and GHI, are designed such that DE = GH, EF = HI, and angle E = angle H. Are the sails congruent? Provide the reasoning based on triangle congruence criteria.

• No, the sails are congruent only if they have the same area.

• No, the sails are not congruent because they have different angles.

• Yes, the sails are congruent but only if they are the same color.

• Yes, the sails are congruent.