Given a trapezoid ABCD, diagonals are drawn, the point where they intersect is called O

| February 22, 2021 | education

Given a trapezoid ABCD, diagonals are drawn, the point where they intersect is called O, prove that ABCD is a trapezoid if it is given that AO = 15cm BO = 8cm AC = 27cm DO = 10cm

Let’s determine the length of the OС segment.

OС = AC – AO = 27 – 15 = 12 cm.

In the triangles BOС and AOD, we find the ratio of similar sides.

ОВ / ОD = 8/10 = 4/5.

OС / AO = 12/15 = 4/5.

In the triangles BOC and AOD, the angle BOC = AOD as vertical angles, and the adjacent sides are proportional, then the triangles are similar in two proportional sides and the angle between them.

Then the angle ОВС = ОDC, and since these are cross-lying angles at the intersection of the straight lines ВС and АD of the secant ВD, then ВС is parallel to АD, and then ABCD is a trapezoid, which was required to be proved.



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