Through the point of intersection of the diagonal of the ABCD parallel, a straight line is drawn intersecting

| April 8, 2021 | education

Through the point of intersection of the diagonal of the ABCD parallel, a straight line is drawn intersecting the sides of AD and BC, at points E and F. Find the sides of the parallel if P = 28 cm, AE = 5 cm, PF = 3 cm

Consider two triangles COF and AOE. Let us prove that these triangles are equal. The angles O of both triangles are equal as vertical angles, the sides AO = CO, as half the length of the digonal AC, the angles FCO and EOA are equal as the internal criss-crossing angles at the intersection of parallel lines BC and AD of the secant AC. The triangles are equal in side and two angles, then AE = FC = 5 cm.

Then the sides AD and BC of the parallelogram are equal to BF + FC = 3 + 5 = 8 cm.

AB = CD = (P – AD – BC) / 2 = (28 – 8 – 8) / 2 = 6 cm.

Answer: The sides of the parallelogram are 6 and 8 cm.



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