In a quadrilateral ABCD AB = CD, BC = AD, angle A = 30 degrees. On side BC, point E is taken so that angle CDE = 60 degrees.

| December 5, 2020 | education

In a quadrilateral ABCD AB = CD, BC = AD, angle A = 30 degrees. On side BC, point E is taken so that angle CDE = 60 degrees. Prove that ABCD is a rectangular trapezoid.

Draw a quadrangle ABCD. Draw a straight line from angle D to point E. So we look, we get a right-angled triangle and a right-angled trapezoid. Proof: Consider a quadrilateral ABCD and a triangle CDE. In given it is indicated that: angle A = 30 degrees; AB = CD, BC = AD; the opposite angles and sides in the parallelogram are equal, so the angle C = 30. It is said in the given that CDE = 60, => 60 + 30 = 90 – angle E (straight line). Consider the trapezoid ABED. It is known that the angle A = 30 degrees, but if the angle E in the triangle is 90, then the angle E in the trapezoid will be 90 degrees. The angles of a trapezoid add up to 360 degrees.



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