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 Δ PQR is double the perimeter of Δ ABC.

Question

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 &#x394; PQR is double the perimeter of &#x394; ABC.

Philoid · Accepted Answer

Given,

In ΔABC

ABCQ and ARBC are parallelograms,

BC = AQ &

BC = AR

AQ = AR (A is mid point of QR)

Similarly B and C are the mid point of PR and PQ

AB =

BC =

AC =

PQ = 2AB

QR = 2BC

PR = 2CA

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

Perimeter of PQR = 2(Perimetre of ΔABC)

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 ΔPQR is double the perimeter of ΔABC.