ABCD is a parallellogram. Draw its diagonals to intersect at O. Prove that the diagobals bisecs its others.
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Answer:
We know that ABCD is a parallelogram whose diagonals intersect each other at O
Consider △AOE and △COF
We know that ∠CAE and ∠DCA are alternate angles
From the figure we know that the diagonals are equal and bisect each other
AO=CO
therefore it is proved that OE=OF
We know that ∠AOE and ∠COF are vertically opposite angles
∠AOE=∠COF
By ASA congruence criterion
△≅COF
OE=OF (c.p.c.t)
Answered by
1
Answer:
We know that ABCD is a parallelogram whose diagonals intersect each other at O
Consider △AOE and △COF
We know that ∠CAE and ∠DCA are alternate angles
From the figure we know that the diagonals are equal and bisect each other
AO=CO
therefore it is proved that OE=OF
We know that ∠AOE and ∠COF are vertically opposite angles
∠AOE=∠COF
By ASA congruence criterion
△≅COF
OE=OF
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