The bisectors of angles A and B at the lateral side AB trapezoid ABCD intersect at point F. Find AB if AF = 21 and BF = 20
| February 23, 2021 | education
By the property of a trapezoid, the sum of its angles at the lateral side is 180.
Angle (ABC + ВAD) = 180.
Segments BM and AK are the bisectors of the angles at the lateral side, then the sum of the angles (BAF + ABF) = (ABC + BAD) / 2 = 180/2 = 90.
Then in the triangle ABF the angle AFB = (180 – 90) = 90, and therefore the triangle ABF is rectangular.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AF ^ 2 + BF ^ 2 = 441 + 400 = 841.
AB = 29 cm.
Answer: The length of the lateral side AB is 29 cm.
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