Q. 16 4.4( 174 Votes )

If AD and PM are medians of triangles ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that ab/pq = ad/plus or minus

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


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



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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