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PB//DQ if AQ//CP and AB// CD (trapezoid ABCD)

Source: Netherlands - Dutch NMO 1971 p1

January 28, 2023

geometrytrapezoidparallel

Problem Statement

Given a trapezoid

ABCD

, where sides

AB

and

CD

are parallel; the points

P

on

AD

and

Q

on

BC

lie such that the lines

AQ

and

CP

are parallel. Prove that lines

PB

and

DQ

are parallel.

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