In an isosceles trapezoid ABCD (AD- larger base, BC-a, AD-b) BE-height. Find AE and ED.
| April 10, 2021 | education
Let’s draw one more ВН height.
Quadrangle ВСЕН is a rectangle, since BH and CE are the height of the trapezoid, then НЕ = ВС = a cm.
In right-angled triangles ABН and CDE, the hypotenuse AB and CD are equal to k. To the lateral sides of the trapezium, and the angle BAН = CDE as angles at the base of an isosceles trapezium, then triangles ABN and CDE are equal in hypotenuse and stroma angle. Then AH = DE.
AH = AD – DH = AD – BC – AН.
2 * AH = AD – BC = (b – a).
AH = ED = (b – a) / 2.
AE = AH + НЕ= AH + BC = AH + a = ((b – a) / 2) + a = (b – a + 2 * a) = 2 = (a + b) / 2.
Answer: AE = (a + b) / 2, ED = (b – a) / 2.
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