SOLUTION: ABCD is a trapezium in which AB is parallel to DC. The bisectors of angles A and D intersect at E. Prove that angle AED=90 degrees.

Algebra ->  Points-lines-and-rays -> SOLUTION: ABCD is a trapezium in which AB is parallel to DC. The bisectors of angles A and D intersect at E. Prove that angle AED=90 degrees.      Log On


   

Question 1118689: ABCD is a trapezium in which AB is parallel to DC. The bisectors of angles A and D intersect at E. Prove that angle AED=90 degrees.
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


Since AB and CD are the parallel sides, angles A and D are consecutive angles with an angle sum of 180 degrees.

Since AE bisects angle A and DE bisects angle D, the sum of angles EAD and EDA is half of 180 degrees, or 90 degrees.

In triangle ADE that means angle AED is 90 degrees.