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

| March 15, 2021 | education

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

By the condition AD + BC = 70, then AD = 70 – BC.

Let us prove that triangle BOC is similar to triangle AOD.

Angle BOC = AOD as vertical angles at the intersection of straight lines BD and AC.

The angle BCO of the triangle BOC is equal to the angle OAD of the triangle AOD as criss-crossing angles at the intersection of parallel lines BC and AD secant AC.

Then the BOC triangle is similar to the AOD triangle in two angles, the first sign of the similarity of triangles.

Then AD / BC = DO / BO.

AD / (70 – AD) = 9/5.

5 * AD = 70 * 9 – 9 * AD.

14 * AD = 630.

AD = 45 cm.

BC = 70 – 45 = 25 cm.

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



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