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
Answers
Answered by
4
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.
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