In an isosceles trapezoid, the diagonal is perpendicular to the lateral side and is the bisector

| June 23, 2021 | education

In an isosceles trapezoid, the diagonal is perpendicular to the lateral side and is the bisector of one of the corners of the trapezoid. Determine in what ratio the diagonal of the trapezoid is divided by the point of their intersection.

Let’s denote the angle CAD through X. The sum of the opposite angles of the trapezoid is 180.

Then: 180 = 90 + 3 * H.

3 * X = 90.

X = 30.

Consider a triangle ADB, in which the angle A = 30, and the angle D = 90, then BD = AB / 2.

The CDB triangle is equilateral at the same angles at the base of the CB. Then CD = BD = AB / 2.

Since the point of intersection of the diagonals of the trapezoid is the apex of similar triangles, the triangles COD and AOB are similar.

According to the properties of similar triangles, CD / AB = 1/2 = CO / OV = DO / OA.

Answer: The diagonals at the intersection point are divided by a ratio of 1/2.



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