# AB and CD are perpendiculars to line BD, points A and C are on opposite sides of line BD.

AB and CD are perpendiculars to line BD, points A and C are on opposite sides of line BD. Prove that BC is parallel to AD if AB = CD.

The ВD and ВDС triangles are rectangular, since AB and СD are perpendicular to the ВD by condition.

The side of the ВD in triangles is common, AB = DС by condition.

Then the AВD and ВDС triangles are equal in two legs – the first sign of right-angled triangles. Then AD = BC.

In the AВСD quadrangle, opposite sides are pairwise equal, then it is a parallelogram. In a parallelogram, the opposite sides are parallel, then the BP is parallel to the aircraft, which was required to be proved.

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