Question

Your Turn: In the diagram, AB = 12, BX = 2.5, and DX = 5. Find CD. Show all work. *

Answer 1

CD = 24 Triangles ABX and CDX are similar triangles. So the ratio of lengths between corresponding legs of the triangles will have the same value. You know that they're similar triangles because both of them are right triangles (so you know that one angle is the same in both) and that arc draw on both angles AXB and CXD indicate that those angles match as well. That tells you there's a second angle that's matching in both triangles, and because two of the angles match, you also know that the unmarked angle matches as well since all the angles in a triangle have to add up to 180 degrees. So you know that AB/CD = BX/DX. Substitute known values and you get AB/CD = BX/DX 12/CD = 2.5/5 Now solve for CD 12/CD = 2.5/5 12/CD = 1/2 24/CD = 1 24 = 1 * CD 24 = CD So the value of CD is 24.