The height of an isosceles trapezoid drawn from apex C is the length of the base AD

univerkov | September 7, 2021 | education

The height of an isosceles trapezoid drawn from apex C is the length of the base AD on a segment of length 2 and 9, find the length of the base BC.

Given: ABCD – isosceles trapezoid, CH height, AH = 9 cm, НD = 2 cm. Find BC -? Solution: From the top B we lower the height BF to the base AD. Heights BF = CH, AB = CD, angle A is equal to angle D as trapezoid ABCD is isosceles. So triangles ABF is equal to triangle CDH, then AF = HD = 2 cm. Then FH = AD – AF – HD; AD = AH + HD, AD = 9 + 2 = 11; FH = 11 – 2 – 2 = 7 (see) as the BCHF figure is a rectangle.
Segment BC = FH = 7 cm.

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