The intersection point of the trapezoid diagonals divides them into 5cm and 9cm segments

| May 18, 2021 | education

The intersection point of the trapezoid diagonals divides them into 5cm and 9cm segments. find the bases of the trapezoid if their sum is 70cm.

Let us prove that the triangles BOC and AOD are similar. The BOC angle is equal to the AOD angle as the vertical angles at the intersection of the AC and BD diagonals.

The OBC angle is equal to the ADO angle as the intersecting angles at the intersection of parallel straight lines ВС and АD of the secant ВD. Then the triangles BOC and AOD are similar in two angles.

Let the length of the base BC = X cm, then AD = (70 – X) cm.

In similar triangles: ВС / ОВ = АD / ОD.

X / 5 = (70 – X) / 9.

350 – 5 * X = 9 * X.

14 * X = 350.

X = BC = 350/14 = 25 cm.

AD = 70 – 25 = 45 cm.

Answer: The lengths of the bases are 25 cm and 45 cm.



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