Question

Given the parallelogram TVWY shown above, determine how triangles TUZ and WXV can be shown to be similar. A. Since ZTU VWX and VX = XW, the triangles are similar by angle-side. B. Since TUZ WXV and TU = UZ, the triangles are similar by angle-side. C. Since TUZ VWX and ZTU WXV, the triangles are similar by angle-angle. D. Since TUZ WXV and ZTU VWX, the triangles are similar by angle-angle.

Answer 1

Notice that triangles TUZ and WXV have an angle with the same measure; therefore, we need two additional corresponding similar angles, or two corresponding similar sides, or one side and an angle to prove similarity.

Options A is not possible since it would imply that triangle TUZ has two 90°-inner angles.

Option B states a relation between two sides of triangle TUZ, not between two sides (one of each triangle). Option B cannot be the answer.

According to the figure, angles TUZ and WXV have to be congruent; therefore, option C cannot be the answer.

The only valid alternative is option D, option D is the answer.