A straight line is drawn through the point of intersection of the diagonals of the parallelogram ABCD

| March 18, 2021 | education

A straight line is drawn through the point of intersection of the diagonals of the parallelogram ABCD, intersecting the sides AD and BC at points E and F. Find the sides of the parallelogram if its perimeter = 28cm, AE = 5cm, BF = 3cm.

Let us prove that the triangle BOF and DOE are equal.

Angle BOF = DOE as cross-lying angles at the intersection of lines FE and BD. The angle ОDE is equal to the angle ОВF as criss-crossing angles at the intersection of parallel lines ВС and АD of the secant ВD.

The segment ОВ = ОD, since the diagonals of the parallelogram at the point of intersection are divided in half. Then the triangle BOF = DOE along the side and two adjacent corners. Then DE = BF = 3 cm.

Side length AD = AE + DE = 5 + 3 = 8 cm.

Determine the length of the side AB through the perimeter.

P = 2 * (AB + AD).

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

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



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