If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
We are given that ZT is parallel to XY. This means that ∠ WZT is congruent to ∠ WXY and ∠ ZTW is congruent to ∠ XYW, as they are corresponding angles. This means that two angles of △ WZT are congruent to two angles of △ WXY. Therefore, by the Angle-Angle Similarity Theorem △ WZT and △ WXY are similar triangles.
△ WZT ~ △ WXY
Finding the Measures
Using our similarity statement from above, we can identify two pairs of corresponding sides that will help us find the requested lengths.
ZT corresponds with XY
WT corresponds with WY
Recall that corresponding segments of similar figures will have proportional lengths. As we have been given expressions for the lengths of these sides, we can write a proportion.
ZT/XY = WT/WY
⇕
10/16 = x/20
Let's solve this equation to find x.
