Question

5. Given that AABC - APQR, CM and RN are respectively the medians of AABC
APOR. Prove that
C С
(1) AAMC - APNR
CM
AB
R
RN
PQ
(ii) ACMB - ARNO
6. Diagonala
A​

Answer 1

Step-by-step explanation:

ANSWER

ΔABC and ΔPQR

CM is the median of ΔABC and RN is the median of $ΔPQR

Also,

ΔABC∼ΔPQR

To Prove: ΔAMC∼ΔPNR

Proof:

CM is median of ΔABC

so, AN=MB=

2

1

AB......(1)

Similarly, RN is the median of ΔPQR

So, PN=QN=

2

1

PQ......(2)

Given,

ΔABC∼ΔPQR

PQ

AB

=

QR

BC

=

RP

CA

(Corresponding sides of similar triangle are proportional)

PQ

AB

=

RP

CA

2PN

2AM

=

RP

CA

{from (1) & (2)}

PN

AM

=

RP

CA

...........(3)

Also,

Since ΔABC∼ΔPQR

∠A=∠B (corresponding angles of similar triangles are equal)

In ΔAMC∼ΔPNR

∠A=∠P From (4)

PN

AM

=

RP

CA

from (3)

Hence by S.A.S similarly

ΔAMC∼ΔPNR

Hence proved.