# If ABCD is a parallelogram, then prove thatar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC)=ar(Δ ACD) = ar(||gm ABCD)

We know that,

Diagonal of parallelogram divides it into two quadrilaterals.

Since,

AC is the diagonal

Then, Area (ΔABC) = Area (ΔACD)

= Area of parallelogram ABCD (i)

Since,

BD is the diagonal

Then, Area (ΔABD) = Area (ΔBCD)

= Area of parallelogram ABCD (ii)

Compare (i) and (ii), we get

Therefore,

Area (ΔABC) = Area (ΔACD) = Area (ΔABD) = Area (ΔBCD) = Area of parallelogram ABCD

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Surface Area and Volume of Right Circular Cone37 mins  R D Sharma | Surface Area and Volumes39 mins  Surface Area and Volume of Right Circular Cylinders42 mins  Surface Area and Volume of Spheres40 mins  RD Sharma | Surface areas and volumes of Cube & Cuboid33 mins  Quiz | Surface Area and Volumes43 mins  What an Atom holds?41 mins  Types of Present Tense55 mins  Applications of Laws of Motion34 mins  Building blocks of brain27 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 