In the parallelogram ABCD, the diagonal BD and the segment AF (FBC) intersecting BD at point O are drawn.
| August 14, 2021 | education
In the parallelogram ABCD, the diagonal BD and the segment AF (FBC) intersecting BD at point O are drawn. It is known that BO = 6cm, OD = 18cm, BF = 4cm. Find the AD side to the parallelograms ABCD.
Let us prove that the triangles BOF and AOD are similar.
The BOF angle is equal to the AOD angle as the vertical angles formed at the intersection of straight lines BD and AF.
The angle OAD is equal to the angle ОFВ as criss-crossing angles at the intersection of parallel lines ВС and АD of the secant AF. Then the triangles BOF and AOD are similar in two angles.
Then such triangles have AD / BF = OD / OB.
AD / 4 = 18/6.
AD = 4 * 18/6 = 12 cm.
Answer: The length of the side AD is 12 cm.
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