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Mathematics

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ABCD is a parallelogram with diagonals AC and BD intersecting at O

Prove that the diagonals bisect one another

Please Help Itll Be Appreciated And If Possible Ill Give BrainliestABCD Is A Parallelogram With Diagonals AC And BD Intersecting At OProve That The Diagonals Bi class=

Answer :

Ivycoveredwallsgo Ivycoveredwallsgo

Step-by-step explanation:

See the attached image. I numbered angles differently so as not to make an assumption that angles numbered the same are congruent.

[tex]\overline{AB} \parallel \overline{CD}\\\angle1 \cong \angle3[/tex] (alternate interior angles are congruent)

[tex]\overline{AD} \parallel \overline{BC}\\\angle 2 \cong \angle 4[/tex] (alternate interior angles are congruent)

[tex]\overline{AB} \cong \overline{CD}[/tex] (opposite sides of a parallelogram are congruent)

[tex]\triangle{ABO \cong \triangle{CDO}[/tex] (ASA - side/angle/side)

[tex]\overline{AO} \cong \overline{CO}\\\overline{BO} \cong \overline{DO}[/tex] (corresponding parts of congruent triangles are congruent)

The diagonals bisect each other!

View image Ivycoveredwalls

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