The bisectors of angles A and B at the lateral side AB of the ABCD trapezoid intersect at point F.
| June 24, 2021 | education
The bisectors of angles A and B at the lateral side AB of the ABCD trapezoid intersect at point F. Find AB if AF = 24, BF = 10.
By the property of the bisectors of the trapezoid drawn from the vertices of the lateral side, a right angle is formed at the point of their intersection. Then the triangle AFB is rectangular, from which, by the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = BF ^ 2 + AF ^ 2 = 10 ^ 2 + 24 ^ 2 = 100 + 576 = 676.
AB = √676 = 26 cm.
Answer: The length of the AB side is 26 cm.
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