Question

if ABCD is a parallelogram.Show that ar(∆ACD)=(∆BDC)
Please answer to this question.

Answer 1

Answer:

Step-by-step explanation:

Given - ABCD is a parallelogram

To prove - (ΔACD)=(ΔBDC)

Construction - draw a line from A to C and B to D with the intersection point as O

Prove -

In triangle AOC and BOC

OB=OC                            (diagonals of parallelogram bisects each other)

∠AOC=∠BOC                             (vertical opposite angles)

OA=OC                            (diagonals of parallelogram bisects each other)

ΔAOC=ΔBOC                 (by SAS )

Now,

adding the ar(ΔCOD) to both the side

(ΔAOC) + (ΔCOD) = (ΔBOC) + (ΔCOD)

(ΔACD)=(ΔBDC)

∴proved