P and Q are respectively the mid points of side AB and BC of a triangle ABC and R is the mid point of AP show that,
{1} ar(PQR)= 1/2 ar(ARC)
{2} ar (RQC)=3/8 ar(ABC)
3) ar (pBQ) = ar(ARC)
Given that: P and Q are the mid points of side AB and BC of a triangle ABC and R is the mid-point of AP
To prove:
Construction: join PQ , RQ and RC
Proof:
(3)
CR is a median of
Also, CP is a median of
From (1) and (2), we get,
PQ is a median of,
From (3) and (4), we get,
Hence,
(1)
Since QP and QR medians of triangles QAB and QAP
And
From (6) and (7), we get,
From (5) and (8), we get,
Hence,
(2) Since CR is a median of,
…… (1)
Since RQ is median of,
Hence,