Question

in the adjoining figure, ABC is a triangle. Through
B and C lines are drawn parallel to BC, CA and
AB respectively, which forms a triangle PQR. Show that
2(AB + BC + CA) = PQ + QR + RP.​

Answer 1

Answer:

Step-by-step explanation:

Given: ABC is a triangle. AB II RP, BC II RQ and CA II PQ  

To Prove: 2(AB + BC + CA) = PQ + QR + RP.

Proof:

Since, AB II RP, BC II RQ and CA II PQ

Therefore ABCR is a IIgm, ABPC is a IIgm and AQBC is a IIgm.

=>     AB = RC and AR = BC (as ABCR is a IIgm)

        AB = CP and  AC = BP (as ABPC is a IIgm)

        BC = AQ and AC = QB (as AQBC is a IIgm)      

PQ + QR + RP = (BP + BQ) + (RA + AQ) + (RC + CP)

                        = (AC + AC)  + (BC + BC) + (AB + AB)

                         = 2AC + 2BC + 2AB

                         =2 (AB +BC + CA)

Hence Proved.

Answer 2

Step-by-step explanation:

Mark me as the brainliest