AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

State true or false.

If in ∆ABC, D is the midpoint of AB and P is any point on BC. If CQ ‖ PD meets AB in Q, then ar(∆BPQ) = ar(∆ABC).

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given that If in ∆ABC, D is the midpoint of AB and P is any point on BC. If CQ ‖ PD meets AB in Q.
We have to check if ar(∆BPQ) =

\frac{1}{2}

ar(∆ABC).

Considering the given figure, In quadrilateral DPCQ,
Area of ∆DPQ= Area of ∆DPC... (i)
Considering equation (i) and adding area of ∆BDP on both sides,

⇒

Area of ∆DPQ+ Area of ∆BDP= Area of ∆DPC+ Area of ∆BDP

⇒

Area of ∆BPQ= Area of ∆BCD ... (ii)
Since D is the midpoint of BC, and CD is the median.
Therefore, Area of ∆BCD= Area of ∆ACD=

12

Area of ∆ABC ... (iii)
Observe equation (ii) and (iii).
Subtracting equation (iii) from equation (i),
Since, Area of ∆BCD=

12

Area of ∆ABC
Therefore, Area of ∆BPQ=

12

Area of ∆ABC
Thus the statement is true.
Therefore, option 1 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!