In an isosceles trapezoid ABCD with bases BC = 4 and AD = 8, the height BH was drawn

| August 18, 2021 | education

In an isosceles trapezoid ABCD with bases BC = 4 and AD = 8, the height BH was drawn. Find the length of the segment AH?

The first way.

We will construct the heights BH and CK of the trapezoid ABCD.

The quadrilateral BHKC is a rectangle, then HK = BC = 4 cm, and triangles ABH and CDK are rectangular.

In right-angled triangles ABH and CDK, the hypotenuse AB and CD are equal, since the trapezoid is isosceles, and, accordingly, the angle BAH = CDK, then the triangles are equal in hypotenuse and acute angle, which means AH = DK = (AD – HK) / 2 = (8 – 4) / 2 = 2 cm.

Second way.

In an isosceles trapezoid, the height drawn to the larger base divides it into two segments, the length of the smaller of which is equal to the half-difference of the bases.

AH = (AD – BC) / 2 = (8 – 4) / 2 = 3 cm.

Answer: The length of the segment AH is 2 cm.



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