You visited us 1 times! Enjoying our articles? Unlock Full Access!

Line Segment That Subtends Equal Angles at Two Other Points

BD is one of ...

Question

BD is one of the diagonals of a quadrilateral ABCD. AM and CN are the perpendiculars from A and C, respectively, on BD. Show that
$a r (q u a d . A B C D) = \frac{1}{2} B D . (A M + C N)$

Open in App

Solution

$a r (q u a d . A B C D) = a r (△ A B D) + a r (△ B C D)$
$a r (q u a d . A B C D) = \frac{1}{2} (B D \times A M) + \frac{1}{2} (B D \times C N)$

$a r (q u a d . A B C D) = \frac{1}{2} B D \times (A M + C N)$

Suggest Corrections

Similar questions

A B C D

A M

C N

B D,

A M = C N

A C

B D

O,

?

BD is one of the diagonals of a quad.ABCD.If $A L ⊥ B D$ and $C M ⊥ B D$ ,show that ar(quad.ABCD)= $\frac{1}{2} \times B D \times (A l + C M)$ .

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that

[Hint: From A and C, draw perpendiculars to BD]

A M

C N

B D

A B C D

△ A M D ≅ △ C N B

Join BYJU'S Learning Program