# D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar(ΔBOE) = ar(Δ ABC)

Join A and D to get AD median

(Median divides the triangle into two triangles of equal area)

Therefore,

Area (ABD) = Area (ABC)

Now,

Join A and E to get AE median

Similarly,

We can prove that,

Area (ABE) = Area (ABD)

Area (ABE) = ABC (Area (ABD) = Area (ABC) (i)

Join B and O and we get BO median

Now,

Area (BOE) = Area (ABE)

Area (BOE) = * Area (ABC)

Area (BOE) = Area (ABC)

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
RD Sharma | Surface areas and volumes of Cube & Cuboid33 mins
Smart Revision | Surface Areas and Volume of Solids31 mins
Quiz | Surface Area and Volumes43 mins
Surface Area and Volume of Right Circular Cylinders42 mins
Surface Area and Volume of Spheres40 mins
What an Atom holds?41 mins
Types of Present Tense55 mins
NCERT | Laws of Motion31 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