Given ABCD – trapezoid, angle A = 90; angle D = 45 smaller base 10 cm and smaller side 10 cm, find a larger base
| April 18, 2021 | education
From the top of the obtuse angle C, draw the height CH.
In a right-angled triangle СНD, the angle СDН, by condition, is equal to 45, then the angle DСН = 180 – 90 – 45 = 45.
Since the angles at the base of the triangle are equal, the triangle DH is isosceles DH = CH = AB = 10 cm.
Quadrangle ABCН is a rectangle, then BC = AH = 10 cm.
Determine the length of the larger base of the trapezoid.
AD = AH + DH = 10 + 10 = 20 cm.
Answer: The length of the AD base is 20 cm.
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