In Parallelogram ABCD o is any point on the diagonal bd .prove that area of triangle OAB=area of triangle COB

Asked by Muruga | 17th Jan, 2018, 04:43: PM

Expert Answer:

 
begin mathsize 16px style Construction colon space Join space AC.
Let space AC space and space BD space intersect space at space straight P.
Now comma space straight P space is space the space midpoint space of space diagonals space AC space and space BD space since space diagonals space of space straight a space parallelogram
bisecteach space other.
rightwards double arrow BP space is space the space median space of space triangle ABC.
rightwards double arrow Area space of space triangle PAB equals Area space of space triangle PCB space space space.... left parenthesis straight i right parenthesis
Similarly comma space OP space is space the space median space of space triangle OAC.
rightwards double arrow Area space of space triangle OAP equals Area space of space triangle OCP space space space space.... left parenthesis ii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
Area space of space triangle PAB plus Area space of space triangle OAP equals Area space of space triangle PCB plus Area space of space triangle OCP
rightwards double arrow Area space of space triangle OAB equals Area space of space triangle OBC end style

Answered by Rashmi Khot | 18th Jan, 2018, 10:27: AM