Find Side of Trapezoid

In the figure, AB and CD are parallel, the measure of angle D is twice that of angle B, AD is of length a and CD is of length b. What is the length of AB in terms of a and b?

  1. a/2 + 2b
  2. 3b/2 + 3a/4
  3. 2ab
  4. 4ba/2
  5. a + b


Show/Hide Solution

Draw DE to bisect ∠D. Then D1 = D2 = ∠B
∠B + ∠C = 180°, so D2 + ∠C = 180° and ED || BC.
BCDE is a parallelogram → EB = b.
E1 = B (corresponding angles) → E1 = D1 = D2,
so △AED is isosceles → AE = a
AB = AE + EB = a + b.
The answer is (e).


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