Question

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 1

The answer to this question can be described as follows:

Explanation:

• In Additional
  `\angle`A and B implies, that ABCD is a parallelogram. So, there diagonals AC and BD were intersecting.
• 
  `\angle` AKO and CMO are similar to BC, for they are congruent. There are, therefore, congruent
  `\angle` of MCO and KAO.
• The AOK and COM triangles are at least identical, so these triangles are congruent because the bisects AC are of BD .
• Then KO and MO are congruent since they are matching congrue sides, that's why MO≅KO is its points.