1.2. Two facts from geometry 7 1.2.2. Proposition. If ΔABC and ΔXY Z are similar triangles with ∠A = ∠X, ∠B = ∠Y , and ∠C = ∠Z, then the ratios of corresponding sides are equal. That is, |AB| |AC| = |XY | |XZ| , |AB| |BC| = |XY | |Y Z| , |BC| |AC| = |Y Z| |XZ| . Exercises 1. Find all the angles in Figure 1.2.1 that are equal to ∠BPE. 2. Suppose that the lines AB and CD are parallel as in Figure 1.2.2, and that the lines OQ and OS are drawn. Show that ΔOQS and ΔOPR are similar. Figure 1.2.2 Figure 1.2.3 3. Suppose that in Figure 1.2.3 |AB| = 4, |BC| = 8, and |XZ| = √ 3. Find the lengths of the remaining sides in the two triangles. 4. In Figure 1.2.3, suppose that |AB| = 6, |AC| = 8, |BC| = 10, and |XY | = 3. Find |XZ| and |Y Z|.

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2010 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.