Предмет: Геометрия, автор: Ozzyxolod

В выпуклом четырехугольнике АВСD АВ=9 см, ВС =8 см, CD = 16 см, AD = 6 см, ВD = 12 см. Докажите, что ABCD трапеция

Ответы

Автор ответа: MM18

Два треугольника - ABD и BCD подобны, их стороны 6,9,12 и 8,12,16 пропорциональны( 6/8 = 9/12 = 12/16, 3/4 = 3/4 = 3/4). Поэтому угол ABD лежащий против стороны AD = 6 в треугольнике ABD, ревен углу BDC, лежащему напротив стороны ВС = 8 в треугольнике BDC - накрест лежащие углы при прямых AB и CD, и секущей BD.
Значит AB II CD.

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