Q. 164.3( 253 Votes )

If AD and PM are

Answer :

It is given that ΔABC is similar to ΔPQR



 
Given: Δ ABC ~ Δ PQR

AD and PM are medians 
We know that the corresponding sides of similar triangles are in proportion

        ..........eq(i)

And also the corresponding angles are equal

A = P

B = Q

C = R           ..........eq(ii)


Since AD and PM are medians, they divide their opposite sides in two equal parts


BD = and,


QM =          .......eq(iii)


From (i) and (iii), we get


(iv)


In ΔABD and ΔPQM,


B = Q [Using (ii)]


[Using (iv)]


ΔABD ΔPQM (Since two sides are proportional and one angle is equal then by SAS similarity)



Hence, Proved

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