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Question

ΔABC and ΔPQR are two similar triangles shown in the figure. AM and PN are the medians on ΔABC and ΔPQR respectively. Which of the following statements is true?


A
ΔABM ~ ΔPQR
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B
ΔAMC ~ ΔPNR
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C
ΔABM ~ ΔPQN
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D
ΔABM ~ ΔPNQ
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Solution

The correct options are
B ΔAMC ~ ΔPNR
C ΔABM ~ ΔPQN
Since ΔABC and ΔPQR are similar, ratio of corresponding sides is same.

ABPQ=BCQR=CARP

and A=P,B=Q and C=R

Medians AM and PN divide BC and QR into two equal parts, respectively.

BM=BC2,QN=QR2

In ΔABM and ΔPQN,

we know that ABPQ=BCQR

ABPQ=2BM2QN

ABPQ=BMQN

and B=Q

ΔABMΔPQN (by SAS similarity criterion)

Similarly, ΔAMCΔPNR (by SAS similarity criterion)

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