In the trapezoid, the larger base is 18 cm, the angles for the larger base are 530 and 370.

| April 11, 2021 | education

In the trapezoid, the larger base is 18 cm, the angles for the larger base are 530 and 370. Find the distance from the point of intersection of the extensions of the lateral sides to the middle of the larger base.

Let us determine the angle at the vertex K of the triangle AKD formed by extending the lateral faces of the trapezoid ABCD.

Angle AKD = 180 – ∠ КАD – ∠ КDА = 180 – 53 – 37 = 900.

Consequently, triangle AKD is rectangular, and its angle AKD is straight.

Since, according to the condition, the CM divides the base of the AD trapezoid in half, the CM is the median of a right-angled triangle, drawn from a right angle.

According to the property of the median of a right-angled triangle, drawn from a right angle, the median is equal to half the length of the hypotenuse, therefore, KM = AD / 2 = 18/2 = 9 cm.

Answer: KM = 9 cm.



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