The bases of the trapezoid are 8 cm and 14 cm. Find the line segments where the trapezoid’s diagonal divides the midline.

univerkov | May 26, 2021 | education

The diagonal AC of the trapezoid ABCD divides the trapezoid into two triangles ABC and ACD.

Consider a triangle ABC. Since point K is the middle of AB, and KO is parallel to BC, then KO is the middle line of the triangle.

The length of the midline of the triangle is half the length of the base parallel to the midline. KO = BC / 2 = 8/2 = 4 cm.

Consider triangle ACD. Since point M is the middle of CD, and MO is parallel to AD, then MO is the middle line of triangle ACD.

Then OM = AD / 2 = 14/2 = 7 cm.

Answer: The length of the segments is 4 cm and 7 cm.

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