1. ABC is a triangle and through A,B,C lines are drawn parallel
to BC, CA and AB respectively intersecting at P, Q and R.
Prove that the perimeter of APQR is double the perimeter
of triangle ABC
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1. ABC is a triangle and through A,B,C lines are drawn parallel
to BC, CA and AB respectively intersecting at P, Q and R.
Prove that the perimeter of APQR is double the perimeter
of triangle ABC
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Step-by-step explanation:
Clearly, ABCQ and ARBC are parallelograms.
∴BC=AQ and BC=AR
⇒AQ=AR
⇒A is the mid-point of QR.
Similarly, B and C are the mid-points of PR and PQ respectively.
∴AB=
2
1
PQ,BC=
2
1
QR and CA=
2
1
PR
⇒PQ=2AB,QR=2BC and PR=2CA
⇒PQ+QR+RP=2(AB+BC+CA)
⇒ Perimeter of ΔPQR=2 (Perimeter of ΔABC)
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