SOLUTION: The parallel sides of trapezoid ABCD are AD and BC. Given that sides AB, BC, and CD are each half as long as side AD, find the size of angle D.
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Question 147598: The parallel sides of trapezoid ABCD are AD and BC. Given that sides AB, BC, and CD are each half as long as side AD, find the size of angle D. Answer by Fombitz(32388) (Show Source):
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Length of AB = x
Length of BC = x
Length of CD = x
Length of AD = 2x
Draw two perpendicular lines from BC to AD at points B and C.
These create new line BG and CH, and break up AD into AG, GH, and HD.
The triangles ABG and CDH are right triangles and from the diagram BC=GH=x.
Now you have a right triangle with hypotenuse of x and an adjacent leg of x/2.
From trigonometry,
Since ABG and CDH are identical, angle A and angle D are the same.
