In an isosceles trapezoid, the smaller base is equal to the lateral side and 2 times smaller

| May 3, 2021 | education

In an isosceles trapezoid, the smaller base is equal to the lateral side and 2 times smaller than the larger base. Find the corners of this trapezoid.

Let side AB be equal to X cm.

Then, by condition, BC = AB = CD = X cm, and the base AD = 2 * X cm.

Let us draw a line ВН through vertex B, parallel to the lateral side of CD.

The formed quadrangle BCDH is a parallelogram, since its opposite sides are parallel, and then the segment DH = BC = X cm.

Then the segment AH = AD – DH = 2 * X – X = X cm.

In the triangle ABN AB = BН = AH = X cm, the triangle ABН is equilateral, and in an equilateral triangle all angles are 60.

At the trapezoid, the sum of the angles at the sides is 180, then the goal ABC = 180 – ABD = 180 – 60 = 120.

Since the angles at the bases of an isosceles trapezoid are equal, the angle ADC = BAD = 60, the angle BCD = ABC = 120.

Answer: The angles of the trapezoid are 60 and 120.



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