HMMT 二月 2004 · 几何 · 第 6 题
HMMT February 2004 — Geometry — Problem 6
题目详情
- In trapezoid ABCD shown, AD is parallel to BC , and AB = 6 , BC = 7 , CD = 8 , AD = 17. If sides AB and CD are extended to meet at E , find the resulting angle at E (in degrees). E B 7 C 8 6 D A 17
解析
- In trapezoid ABCD shown, AD is parallel to BC , and AB = 6 , BC = 7 , CD = 8 , AD = 17. If sides AB and CD are extended to meet at E , find the resulting angle at E (in degrees). Solution: 90 Choose point F on AD so that BCDF is a parallelogram. Then BF = CD = 8, and AF = AD − DF = AD − BC = 10, so 4 ABF is a 6-8-10 right triangle. The required ◦ 6 angle is equal to ABF = 90 . 2 B 7 C 8 6 8 D A 10 F 7