In the trapezoid abcd, the angle a is a straight line, the angle c is 135 degrees, ab = 5cm, about the bottom

| January 13, 2021 | education

In the trapezoid abcd, the angle a is a straight line, the angle c is 135 degrees, ab = 5cm, about the bottom of the diagonals perpendicular to the side, ad and bc of the base-trapezoid. Find the middle line of the trapezoid.

By condition, the angle C = 135, and the AC diagonal is perpendicular to the СD, then the angle of the ВCA can be determined.
BCA = 135 – 90 = 45.
Consider a right-angled triangle ABC, in which the angle ABC = 90, BCA = 45, therefore the triangle ABC is isosceles, in which AB = CB = 5 cm. Knowing the legs, we define the hypotenuse of the AC by the Pythagorean theorem.
AC^2 = AB^2 + BC^2 = 25 + 25 = 50.
Consider a right-angled triangle AСD, in which angle C = 900, and angle СAD = 90 – BAC = 90 – 45 = 45. Then the triangle AСD is isosceles AС = СD.
Then, according to the Pythagorean theorem, AD^2 = AC^2 + SD^2 = 50 + 50 = 10.
BP = 10 cm.
Determine the length of the middle line of the trapezoid.
KM = (BC + AD) / 2 = (5 + 10) / 2 = 7.5 cm.
Answer: The middle line of the trapezoid is 7.5 cm.



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