In isosceles trapezoid ABCD, points P and K are midpoints of diagonals AC and BC

univerkov | February 2, 2021 | education

In isosceles trapezoid ABCD, points P and K are midpoints of diagonals AC and BC, respectively. Find the length of the segment PK if BC is 9; AD is 25.

Since the points P and K are the middle of the trapezoid diagonals, the PK segment lies on the middle line of the trapezoid. Let’s draw the middle line of the MН. Then in the ВСD triangle the segment KН is its middle line, then KН = BC / 2 = 9/2 = 4.5 cm.

The segment MР is the middle line of the triangle ABC, then MR = BC / 2 = 19/2 = 4.5 cm.

Determine the length of the midline of the trapezoid.

MH = (BC + AD) / 2 = (9 + 25) / 2 = 17 cm.

Then the segment RK = MР- MР – KН = 17 – 4.5 – 4.5 = 8 cm.

Answer: The length of the RK segment is 8 cm.

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