# In a rectangular trapezoid ABCD, the smaller base is perpendicular to the lateral side of AB

October 9, 2021 | education

| **In a rectangular trapezoid ABCD, the smaller base is perpendicular to the lateral side of AB. The AC diagonal is equal to the CD side, ∠CAD = 40. find all the corners of the trapezoid.**

Since, by condition, the diagonal AC is equal to the lateral side of CD, then the triangle ACDD is isosceles, then its angles at the base of AD are equal.

Angle CAD = CDA = (180 – ACD) / 2 = (180 – 40) / 2 = 140/2 = 70.

The ACB angle is equal to the CAD angle as the intersecting angles at the intersection of parallel lines BC and AD secant AC. Then the angle ВСD = АСВ + АСD = 70 + 40 = 110.

The angles BAD and ABC are straight, since the trapezoid is rectangular.

Answer: The angles of the trapezoid are equal: 90, 90, 110, 70.

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