Geometry Question with Solution Yesterday I went over a method for solving certain geometry problems by moving the sides of a figure around. You can see that post here: Moving the Sides of a Figure Around Today I would like to solve yesterday’s problem. Problem: In the figure below, AB = 2, BC = 8, and AD = 10. What is the length of line segment CD ? Solution: The problem becomes much simpler if we “move” BC to the left and AB to the bottom as shown below. We now have a single right triangle and we can either use the Pythagorean Theorem, or better yet notice that 10 = 5 ⋅ 2 and 8 = 4 ⋅ 2. Thus, the other leg of the triangle is 3 ⋅ 2 = 6. So we see that CD must have length 6 – 2 = 4. Remark: If we didn’t notice that this was a multiple of a 3-4-5 triangle, then we would use the Pythagorean Theorem as follows. (x + 2)2 + 82 = 102 (x + 2)2 + 64 = 100 (x + 2)2 = 36 x + 2 = 6 x = 4 More Problems with Explanations If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books. And if you liked this article, please share it with your Facebook friends: Comments comments