Question

Triangle PQR ~ Triangle ABC and PQ:AB=2:5. If PM and AN are the medians, then find the ratio of their corresponding medians.
Please answer with steps (i'll mark as brainliest)

Answer 1

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