In an isosceles trapezoid, the obtuse angle bisector is parallel to the lateral side.

| February 15, 2021 | education

In an isosceles trapezoid, the obtuse angle bisector is parallel to the lateral side. Find the base of the trapezoid if its perimeter is 60 cm and the lateral side is 14 cm.

Since, by condition, the trapezoid is isosceles, then AB = СD = 14 cm. Bisector СН, divides the ВСD angle in half, the angle ВСН =DСН. Angle ВСН = СНD as criss-crossing angles at the intersection of parallel straight lines ВС and AD secant СН. Then the triangle CDН is equilateral СD = CH = DН = 14 cm.

By condition, the bisector CH is parallel to AB, then the quadrangle ABН is a parallelogram, and therefore BC = AН.

Let the segment BC = AH = X cm.

The perimeter of the triangle is: P = AB + BC + SD + DН + AН = 14 + X + 14 + 14 + X = 60.

2 * X + 42 = 60.

2 * X = 60 – 42 = 18 cm.

X = BC = AH = 18/2 = 9 cm.

AD = AН + DН = 9 + 14 = 23 cm.

Answer: The bases of the trapezoid are 9 cm and 23 cm.



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