SOLUTION: In a quadrilateral ABCD where AB║DC point O is the intersection of its diagonals, ∠A and ∠B are supplementary. Point M∈BC and point K∈AD, so that O&#8

Algebra ->  Geometry-proofs -> SOLUTION: In a quadrilateral ABCD where AB║DC point O is the intersection of its diagonals, ∠A and ∠B are supplementary. Point M∈BC and point K∈AD, so that O&#8      Log On


   

Question 1117075: In a quadrilateral ABCD where AB║DC point O is the intersection of its diagonals, ∠A and ∠B are supplementary. Point M∈BC and point K∈AD, so that O∈MK. Prove that MO ≅KO .
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Angles A and B supplementary means ABCD is a parallelogram; so diagonals AC andBD bisect each other.

Angles AKO and CMO are congruent, because AD is parallel to BC. For the same reason, angles MCO and KAO are congruent.

So triangles AOK and COM are at least similar; then since BD bisects AC those triangles are congruent.

Then KO and MO are congruent because they are corresponding sides of congruent triangles.