A straight line AM is drawn through the vertex A of the base AD of trapezoid ABCD

| April 27, 2021 | education

A straight line AM is drawn through the vertex A of the base AD of trapezoid ABCD, parallel to the lateral side of CD and intersecting the midline PT of the trapezoid at point K. Find the difference between the lengths of the segments TC and PK, if BC is 25, AD is 13 and point T lies on the lateral side of CD.

Determine the length of the midline of the trapezoid.

PT = (BC + AD) / 2 = (25 + 13) / 2 = 38/2 = 19 cm.

Since AM, by condition, is parallel to CD, and AD is parallel to BC as the base of the trapezoid, then the quadrangle AMCD is a parallelogram, then MC = AD = 13 cm. The TK segment is parallel to AD and MС, then TK = AD = 13 cm.

Determine the length of the segment ВM.

ВМ = ВС – СМ = 25 – 13 = 12 cm.

In triangle ABM, segment PK is the middle line of the triangle, then its length is equal to half the base of BM.

PK = BM / 2 = 12/2 = 6 cm.

Let’s define the difference between TK and PK.

TK – PK = 13 – 6 = 7 cm.

Answer: The difference between the lengths of the segments TK and PK is 7 cm.



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