triangle PQR - triangle ABC and PQ : AB = 2 : 5 . If PM and AN are the medians , then find the ratio of their corresponding medians.
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Answer:
Given: △ABC∼△PQR
PQ
AB
=
QR
BC
=
PR
AC
(Corresponding sides)
or
PQ
AB
=
2
1
QR
2
1
BC
∠ABC=∠PQR (Corresponding angles)
Now, AD and PM are medians of △ABC and △PQR respectively,
thus, in △ABD and △PQM
∠ABD=∠PQM (Since, △ABC∼△PQR)
PQ
AB
=
QM
BD
(AD and PM are medians)
Thus, △ABD∼△PQM (SAS rule)
Hence,
PQ
AB
=
PM
AD
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