Q : 3    Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Answers (1)


Let ABCD is a parallelogram. So, AB || CD and AD || BC and we know that Diagonals bisects each other. Therefore, AO = OC and BO = OD

Since OD = BO 
Therefore, ar (\DeltaBOC) = ar (\DeltaDOC)...........(a)   ( since OC is the median of triangle CBD)

Similarly, ar(\DeltaAOD) = ar(\DeltaDOC) ............(b)     ( since OD is the median of triangle ACD)

and, ar (\DeltaAOB) = ar(\DeltaBOC)..............(c)           ( since OB  is the median of triangle ABC)

From eq (a), (b) and eq (c), we get

  ar (\DeltaBOC) = ar (\DeltaDOC)= ar(\DeltaAOD) =  (\DeltaAOB)

Thus, the diagonals of ||gm divide it into four equal triangles of equal area.

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions