Geometry and TrigonometryMediumLength in a triangle cut by a parallel line
Geometry and Trigonometry practice question
In triangle ABC, point D is on side AB and point E is on side AC such that DE is parallel to BC. AD = 4, DB = 2, and BC = 9. What is the length of DE?
Answer: 6
DE ∥ BC makes triangle ADE similar to triangle ABC with ratio AD/AB = 4/6 = 2/3. So DE = (2/3)(9) = 6.
Common wrong answers
- If you answered 3
- 3 uses DB/AB = 2/6, the wrong segment.
- If you answered 18
- 18 uses AD/DB = 2 as the ratio; the ratio must compare AD to the whole side AB.
- If you answered 4.5
- 4.5 halves BC, as if AD were half of AB; AD/AB is 4/6, not 1/2.
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