In an isosceles trapezoid, the height drawn from the apex of the obtuse angle divides the larger base of the trapezoid

In an isosceles trapezoid, the height drawn from the apex of the obtuse angle divides the larger base of the trapezoid into 6cm and 15cm segments. Find the base of the trapezoid.

The larger base is equal to the sum of the segments into which the height divides it. AD = AH + DH = 15 + 6 = 21 cm.

Let’s draw the height BK. Triangles ABK and CDH are equal in hypotenuse and acute angle, AB = CD, angle BAK = CDH since the trapezoid is isosceles. Then AK = DH = 6 cm, and KH = (AD – AK – DH) = 21 – 6 – 6 = 9 cm.

A quadrilateral BСNK is a rectangle, then BC = KH = 9 cm.

Answer: The bases of the trapezoid are 9 cm and 21 cm.