In the given triangle ABC, P, Q and R are the midpoints
of BC, CA and AB respectively. Given that BP = 3.5 cm,
AC = 3.8 cm and PQ = 2.7 cm, find the values of
(a) RQ, (b) RP, (c) AR, (d) AB.
Figure is attached.
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Answer:Given
ABC is a Triangle.
P is the m.p of BC
Q is the m.p of CA
R is the m.p of AB
To prove
XY = BC
Proof
In ΔABC
R is the midpoint of AB.
Q is the midpoint of AC.
∴ By Midpoint Theorem,
RQ║BC
RQ║BP → 1 [Parts of Parallel lines]
RQ = BC → 2
Since P is the midpoint of BC,
RQ = BP → 3
From 1 and 3,
BPQR is a Parallelogram.
BQ and PR intersect at X
Similarly,
PCQR is a Parallelogram.
PQ and CR intersect at Y.
X and Y are Midpoints of sides PR and PQ respectively.
In ΔPQR
X is the midpoint of PR
Y is the midpoint of PQ
∴ By Midpoint Theorem,
XY = RQ
From 3,
XY = + BC
XY = BC
Hence Proved.
Step-by-step explanation:
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