Q. 35.0( 1 Vote )

In m ABCD, M is the mid-point of . and intersect in N. Prove that DN = 2MN.

Answer :

In ABCD, M is the mid-point of. and intersect in N.

To prove : DN = 2MN

Proof: M is the mid-point of BC



In ∆MBN and ∆MCD

BMN CMD (Vertically opposite angles)

MNB MDC (Alternate angles)

The correspondence MBNMCD is a similarity

(from 1)


Now, D-M-N

DN = DM + MN

DN = DM + MN

DN = MN + MN (MD = MN)

DN = 2MN

Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
Champ Quiz | Thales Theorem49 mins
Quiz | Criterion of Similarity of Triangle45 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
How to Ace Maths in NTSE 2020?36 mins
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 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