Exercise 21 Page 370

We want to determine if the seat stays of the bicycle are the same length or not. Let's look at the left and right part of the frame separately. Note that the seat tube is a common element of these parts; this is segment AB on the two diagrams of the frame.

We are given information about the measure of four angles. Since two pairs of angles have the same measure, these are congruent. ∠ ACB&≅ ∠ ADB ∠ ABC&≅ ∠ ABD We can see that triangles △ ABC and △ ABD have two pairs of congruent angles and a common side that is not included between the congruent angles. Hence, as the Angle-Angle-Side (AAS) Congruence Theorem implies, the two triangles are congruent. △ ABC≅△ ABD We know that corresponding parts of congruent triangles are congruent, so the two seat stays are congruent. Since congruent segments have the same measure, this means that the two seat stays are the same length. AC≅AD