Question

If TUVW is an isosceles trapezoid with TU parallel to WV, name a pair of similar triangles. Explain.

Answer 1

TXU~VXW by the AA similarity postulate

Answer 2

Alternative interior angle theorem states that when two parallel lines are crossed by transversal line, then the pairs of angles on the inner side each of those two lines but on opposite sides of the transversal are equal.

Given: TUVW is an isosceles trapezoid with TU parallel to WV.

In triangle TXU and triangle VXW.

By alternative interior angle theorem;

`\angle XTU = \angle XVW` [Angle]

`\angle XUT = \angle XWV` [Angle]

AA(Angle-Angle) similar theorem states that the two triangles are similar if they have two corresponding angles that are equal.

then, by AA-similarity theorem;

`\triangle TXU \sim \triangle VXW`

Therefore, a triangle TXU and triangle VXW are similar triangles.