Question

ABC is a triangle where three lines are drawn through the vertices A, B and C parallel to the sides BC, CA and AB respectively, forming PQR. Prove that BC = 1/2PR AC = 1/2 PQ AB = 1/2RQ

Answer 1

Step-by-step explanation:

AQ∥CB and AC∥QB

∴AQBC is a parallelogram

∴BC=AQ (Opposite side of a parallelogram)

∵AR∥BC and AB∥RC

∴ARCB is a parallelogram

∴BC=AR (Opposite side of a parallelogram)

Hence A is the midpoint of QR

Similarly B and C are midpoints of PQ and PR respectively

∴AB=

2

1

PRBC=

2

1

QRCA=

2

1

PQ

2AB=PR2BC=QR2CA=PQ

PR+QR+PQ=2(AB+BC+CA)

Therefore,

Perimeter of △ PQR=2[Perimeter of △ABC]

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