ABCD is an isosceles trapezoid, the height BH divides the bases into two segments equal to 4 and 12.

| March 8, 2021 | education

ABCD is an isosceles trapezoid, the height BH divides the bases into two segments equal to 4 and 12. Find the middle line of the trapezoid.

An isosceles trapezoid is a trapezoid whose sides are equal.

The middle line of a trapezoid is the segment that connects the midpoints of the sides.

The length of the midline is equal to half the sum of the lengths of its bases.

Given: ABCD – isosceles trapezoid, BH – height, AH = 4, HD = 12.

Find: the length of the midline of the trapezoid.

Decision:

Let’s agree AD and BC are the bases of the trapezoid, AD is the larger base, AD = AH + HD = 4 + 12 = 16;

BC = 12 – 4 = 8 (perform additional construction, lower the height from the top of C to the base of AD);

Let’s denote the middle line KE. KE = (AD + BC): 2 = (16 + 8): 2 = 12.

Answer: the middle line is 12.



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