The diagonals of the isosceles trapezoid of the trapezoid ABCD are mutually perpendicular

| March 25, 2021 | education

The diagonals of the isosceles trapezoid of the trapezoid ABCD are mutually perpendicular, BH is the height to the greater base of the trapezoid CD a) prove that the triangle BHD is isosceles b) find the area of the trapezoid if its midline is 11.

Since the AC diagonal is perpendicular to the BD diagonal, the triangle AOD is rectangular, the angle AOD = 90.

Trapezium ABCD is isosceles, then its diagonals are equal and at the point of their intersection are divided into equal segments. ОА = ОD, ОВ = OC.

Then the triangle AOD is rectangular and isosceles, then the angle ODA = OAD = 45.

The BHD triangle is rectangular, since BH is the height, and the BDH angle = 45, then the BHD angle = (90 – 45) = 45, which means the BHD triangle is isosceles, which was required to prove.

Since the diagonals of the trapezoid are perpendicular, the middle line of the trapezoid is equal to its height.

KM = ВН= 11 cm, then Savsd = KM * ВН = 11 * 11 = 121 cm2.

Answer: The area of ​​the trapezoid is 121 cm2.



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