Answer :


Let us assume two similar triangles as ΔABC ΔPQR.


Let AD and PS be the medians of these triangles


Then, because ΔABC ΔPQR


(i)


A = P, B = Q, C = R …(ii)


Since AD and PS are medians,


BD = DC = BC/2


And, QS = SR = QR/2


Equation (i) becomes,


…(iii)


In ΔABD and ΔPQS,


B = Q [From (ii)]


[From (iii)]


ΔABD ΔPQS (SAS similarity)


Therefore, it can be said that




From (i) and (iv), we get



and hence,



Hence, proved!


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
view all courses
RELATED QUESTIONS :

<img width=RD Sharma - Mathematics

<img width=RD Sharma - Mathematics

If <img widRD Sharma - Mathematics

The areas of two RD Sharma - Mathematics

The areas of two RD Sharma - Mathematics

In Fig. 4.236, <sRD Sharma - Mathematics

If <img widRD Sharma - Mathematics

If the altitude oRD Sharma - Mathematics

If the areas of tRD Sharma - Mathematics