Question

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(ΔAOD) = ar(ΔBOC). (Hint:Congruent figures have equal area)

Answer 1

intersect each other at 'O'. Prove that ar(ΔAOD) = ar(ΔBOC).… ... ar( ΔBOC). (Hint:Congruent figures have equal area)

Answer 2

given:ABCD is a parallelogram

diagonals bisect each other at O

To prove:ar (triangleAOD)equal to ar(triangleBOC)

proof:In triangle AOD and BOC

angle AOB equal to Angle BOC because vertically opposite angles - equation1

angle DAO equals to angle OCB because alternate angles - equation2

angle DAO equals to angle OBC because alternate angles - equation3

by AAA criteria

Triangle AOD IS congruent to triangle BOC

hence hint is given that congruent figures have equal area

Therefore ar( triangle AOD) equal to ar ( triangle BOC)

HENCE PROVED