The diagonal AC of trapezoid ABCD is equal to the lateral side of CD, perpendicular
July 15, 2021 | education
| The diagonal AC of trapezoid ABCD is equal to the lateral side of CD, perpendicular to it, and bisects the angle BAD. Find the corners of the trapezoid.
Consider a triangle ACD.
Since by the condition of the problem AC = CD and AC, CD are perpendicular,
then the triangle ACD is right-angled and isosceles.
Consequently, the angles at its hypotenuse are equal to 45 degrees.
Hence, CDA = 45 ° and BCD = 180 ° – 45 ° = 135 °.
Since AC is the bisector of the BAD angle, CAB = CAD = 45 °.
Hence, BAC = 2 * CAD = 2 * 45 ° = 90 °.
Then ABC = 180 ° – BAC = 180 ° – 90 ° = 90 °.
So, the angles A, B, C, D of the trapezoid are equal: 90 °, 90 °, 135 °, 45 °.
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