The heights of an isosceles trapezoid divide it into a square and 2 isosceles triangles

| July 15, 2021 | education

The heights of an isosceles trapezoid divide it into a square and 2 isosceles triangles, the side is 4√2. find the bases and obtuse angle?

Since, by condition, triangles ABH and CDK are isosceles, then AH = BH = CK = DK.

Since one of the angles of the triangle is a straight line, the angle AHB = CKD = 90, then the angle BAН = ABH = KCD = CDK = 45.

Determine the length of the legs of isosceles triangles.

AH = AB * Sin45 = 4 * √2 * √2 / 2 = 4 cm.

Then AH = KD = BH = CK = 4 cm.

Since, according to the condition, НBСК is a square, then BC = НК = ВН = DК = 4 cm.

Determine the length of the larger base. AD = AH + НK + DK = 4 + 4 + 4 = 12 cm.

Determine the length of the midline of the trapezoid.

MR = (BC + AD) / 2 = (4 + 12) / 2 = 8 cm.

Since the acute angles in triangles are 45, the obtuse angle of the trapezoid will be 45 + 90 = 135.

Answer: The length of the midline of the trapezoid is 8 cm, the obtuse angle of the trapezoid is 135.



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