Question

Show that the diagonals of a parallelogram divide it into four triangle of equal area.

Answer 1

Given:- ABCD is a //gm.

To prove:- ΔAOB ≅ ΔBOC ≅ ΔCOD ≅ ΔDOA

Proof:- In ΔAOB & ΔCOD
LBAO = LDCO (alternate interior angle)
AB = CD (opp. sides are equal)
LABO = LCDO (alternate interior angle)
Therefore, ΔAOB≅ ΔCOD by AAS Congruence criterion.

Similarly,
ΔAOB ≅ ΔBOC ≅ ΔCOD ≅ ΔDOA

Answer 2

Hi friend..
Here is your ANSWER



➡️✴️✴️SOLUTION✴️✴️⬅️

DIAGONALS DIVIDE the PARALLELOGRAM INTO 4 TRIANGLES such that

Pair of opposite triangle are congruent..

We know that diagonals of a parallelogram bisect each other.

When you consider ∆ABC , BO is median

So median divide the triangle into 2 equal triangles of equal area.

So all the 4 smaller triangles are equal in area.

When you see pair of opposite triangles

They are congruent so the called it as 4 congruent triangles.


I hope it will help
✌️☺️