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.

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(13200) (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.
RELATED QUESTIONS
ABCD is a trapezium in which AB is parallel to DC and ABC=90 (a)Given that AB=(2x-1)cm... (answered by josgarithmetic)

ABCD is a trapezium. The two diagonal AC and BD intersect in O. extended DA and CB... (answered by lynnlo)

ABCD is a trapezium with right angles at B and C, AB=5cm DC=12cm and the area of the... (answered by greenestamps)

1.M is the mid-point of a line segment AB;AXB and MYB are equilateral triangles on... (answered by KMST)

ABCD is a trapezium such that AB is parallel to CD and angle DAB= angle DBC. Prove that... (answered by greenestamps)

ABCD is a parallelogram in which AB||CD and AD||BC. A and D bisects BC at E and meet DC... (answered by Edwin McCravy)

ABCD is a parallelogram in which AB=6cm & BC=8cm. BC is extended to E such that BC=CE. AE (answered by greenestamps)

abcd is a trapezium in which ab parallel cd.bc and ad are the non parallel sides.it is... (answered by Edwin McCravy)

the figure shows ABCD as a trapezium in which AB=(5x+6) cm, DC= 3x cm and the height... (answered by math175,ikleyn)