Question

21. In the given figure, ABCD is a parallelogram.
Its diagonals intersect at O. Prove that O is
the mid-point of PQ.
[Hint : A∆AOP = ∆QOC)
A
C с​

Answer 1

To prove as (△AOB) = as (△AOD)
proof→ we prove that a diagonal parallelogram with 2 congruent triangle
Thus △ABC≅△CDA
⇒ ar(△ABC) =ar(△CDA)
⇒
2
1
​
(BQ)(AC)=
2
1
​
(os)(Ac)
⇒[BQ=DC]

Now ar(△AOB)=
2
1
​
(AOD)(BQ)
AR(△ADB)=
2
1
​
(ADC)(DS)
⇒
ar(△AOD)
ar(△AOB)
​
=(
DS
BQ
​
)=1
⇒[ar(△AOB)=ar(△AOD)] ---Proved