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AAS Criteria for Congruency

Question 6 ii...

Question

Question 6 (ii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(ii) ar(DCB) = ar(ACB)

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Solution

Let us draw $D N ⊥ A C$ and $B M ⊥ A C$ .
(ii) We obtained,
Area $(Δ D O C) = A r e a (Δ A O B)$
i.e $A r e a (Δ D O C) + A r e a (Δ O C B) = A r e a (Δ A O B) + A r e a (Δ O C B)$
(Adding Area $(Δ O C B)$ to both sides)
$\Rightarrow A r e a (Δ D C B) = A r e a (Δ A C B)$

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Similar questions

Q. Question 6 (ii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(ii) ar(DCB) = ar(ACB)

Q. In the given Figure, diagonals

A C

B D

of quadrilateral

A B C D

O

O B = O D

A B = C D

, then show that :
(i)

a r (D O C) = a r (A O B)

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is a parallelogram.

Q. Question 6 (i)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(i) ar(DOC) = ar(AOB)

Q. Question 6 (i)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(i) ar(DOC) = ar(AOB)

Q. Question 6 (iii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(iii) DA || CB or ABCD is a parallelogram.

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AAS Criteria for Congruency

Standard IX Mathematics

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