You can show that two triangles are similar when certain relationships exist between two or three pairs of corresponding parts. If you know two triangles are similar, then you know their corresponding sides are proportional.
In the diagram below,
Lines with special relationships to the sides and angles of a triangle determine proportional segments. When you know the lengths of some of the segments, you can use a proportion to find an unknown length.
You are making the kite shown below from five pairs of congruent panels. In parts (a)–(d) below, use the given information to find the side lengths of the kite's panels.
ABCD is a kite.
The extended ratio