The angles at the base of the trapezoid are equal and are halved by the diagonals.

| March 17, 2021 | education

The angles at the base of the trapezoid are equal and are halved by the diagonals. The base is 15 cm, the middle line is 10.5 cm. Find the perimeter of the trapezoid.

By condition, the angles at the base of the trapezoid are equal, then the trapezoid ABCD is isosceles, AB = CD.

Since the middle line of a trapezoid is equal to the half-sum of the lengths of its bases, then through it we determine the length of the small base of the trapezoid.

KM = (AD + BC) / 2.

2 * 10.5 = 15 + BC.

BC = 21 – 15 = 6 cm.

According to the condition of the diagonal of the trapezoid, the angles at the base are divided in half, the angle BAC = CAD.

Angle BCA = CAD as criss-crossing angles at the intersection of parallel straight lines AD and BC secant AC.

Then the angle BAC = BCA, and the triangle ABC is isosceles, and the segment AB = BC, and since the trapezoid is isosceles, then CD = AB = BC = 6 cm.

Let’s define the perimeter of the trapezoid:

P = (AB + BC + CD + AD) = 6 + 6 + 6 + 15 = 33 cm.

Answer: The perimeter of the trapezoid is 33 cm.



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