In an isosceles trapezoid, the base of BC is 2 cm, and AD is 5 cm. Find the segments into which the diagonals

| September 24, 2021 | education

In an isosceles trapezoid, the base of BC is 2 cm, and AD is 5 cm. Find the segments into which the diagonals are divided, the point of their intersection, if one of the diagonals is 49 cm. You need a solution, the answer should be 14 cm and 35 cm.

Consider triangles BOC and AOD and prove that they are similar.

Angle BOC = AOD as vertical angles at the intersection of the trapezoid diagonals.

Angle ВСО = ОАD as criss-crossing angles at the intersection of parallel straight lines ВС and АD secant АС, then the triangles are similar in two angles.

Let the length of the segment OC = X cm, then OA = (49 – X) cm.

In similar triangles:

BC / AD = OC / OA.

2/5 = X / (49 – X).

5 * X = 98 – 2 * X.

7 * X = 98.

X = OC = 98/7 = 14 cm.

ОА = 49 – 14 = 35 cm.

Answer: The diagonals are divided into segments of 14 cm and 35 cm.



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