Question

solve this please! :) will be very grateful!

Answer 1

In triangle AOC and BOD
1. AO = BO{given}
CO = DO{given}
angle C = angle D {angles opposite to equal sides are equal}
HENCE,
triangle AOC = triangle BOD (CPCTC).

Answer 2

Given -

In ∆ AOC and ∆ BOD
AO = BO
CO=DO

To Prove -

(I) ∆AOC Congruent to ∆BOD

In ∆AOC and ∆BOD

AO = BO (given)
Angle AOC = Angle BOD (Vertically Opposite Angles)
CO = DO (given)


=> ∆AOC is Congruent to ∆BOD ( By SAS criteria)
____________

(ii) AC = BD

We have proved that ∆AOC is Congruent ∆BOD

=> AC = BD ( CPCT )
____________

(iii) AC || BD

Since , ∆AOD is Congruent to ∆BOD ,

=> angle ACO = Angle BDO ( CPCT)

=> Angle ACO and ∆BDO are interior alternate angles formed by Transversal CD
=> AC||BD

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