Q:

Samantha measured two of the angles in PQR and found that they had measures of 65° and 70°. Then, she measured two of the angles in XYZ and found that they had measures of 65° and 45°. What statement best describes the two triangles? The two triangles cannot be congruent because the angle measures are not the same. The two triangles are congruent because the angle measures in the two triangles are the same. The two triangles may be congruent, but additional information is needed about the third angle in each triangle. The two triangles may be congruent, but additional information is needed about the sides of each triangle.

Accepted Solution

A:
Answer:The two triangles may be congruent, but additional information is needed about the sides of each triangle.Step-by-step explanation:Given that Samantha measured two of the angles in PQR and found that they had measures of 65° and 70°. Then, she measured two of the angles in XYZ and found that they had measures of 65° and 45°.We have by using properties of sum of angles of triangles, angles of PQR are 65, 70, 45 and also same for XYZHence there is a chance that these triangles may be congruent depending on the sides.  We are sure that the angles are congruent hence triangles are similar.  But to prove congruence we must have additional information about sides.The two triangles may be congruent, but additional information is needed about the sides of each triangle.