Isosceles trapezoid height 5. Find the angles of a trapezoid if the diagonal divides the midline into segments 5 and 10.

| February 16, 2021 | education

Consider a triangle ABC. The segment KO of the triangle ABC is the middle line, since it lies on the segment KM, which is the middle line of the trapezoid. Then KO = BC / 2.

BC = 2 * KO = 2 * 5 = 10 cm.

Consider a triangle AСD, which has a midline segment OM, then OM = / AD / 2.

AD = 2 * OM = 2 * 10 = 20 cm.

Since the trapezoid is isosceles, the height of the CH cuts off on the basis of blood pressure segments, the length of the smaller of which is equal to the half-difference of the bases.

DН = (BP – BC) / 2 = (20 – 10) / 2 = 5 cm.

Then the СDН triangle is rectangular and isosceles, CH = DН = 5 cm.

Then the angle СDН = DСН = 45.

In a trapezoid, the sum of the angles at the lateral sides is 180, then the ВСD angle = 180 – СDA = 180 – 45 = 135.

In an isosceles trapezoid, the angles at the base are equal. Angle BCA = СDA = 450, angle ABC = DСВ = 145.

Answer: The angles of the trapezoid are 45 and 135.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.