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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.

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Answer:

The answer to this question can be described as follows:

Step-by-step explanation:

  • In Additional [tex]\angle[/tex]A and B implies, that ABCD is a parallelogram. So, there diagonals AC and BD were intersecting.  
  • [tex]\angle[/tex] AKO and CMO are similar to BC, for they are congruent. There are, therefore, congruent [tex]\angle[/tex] 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.

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