Math, asked by mohantysomyaranjan06, 6 hours ago

the 11. In the adjoining figure, ABC is a triangle. Through A, 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. rer.​

Answers

Answered by IIcuteishuII
10

you're answer is in the picture

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Answered by Anonymous
1

Answer:

From the figure, it is given that, Through A,B and C lines are drawn parallel to BC,CA and AB respectively.

We have to show that 2(AB+BC+CA)=PQ+QR+RP

∵ AB∥RC and AR∥CB

Therefore, ABCR is a parallelogram.

⟹AB=CR and CB=AR (opposite sides of a parallelogram are equal) -------(1)

Similarly, ABPC is a parallelogram (∵AB∥CP and PB∥CA)

⟹AB=PC and AC=PB (opposite sides of a parallelogram are equal) -------(2)

Similarly, ACBQ is a parallelogram (∵BC∥AQ and AC∥BQ)

⟹AC=BQ and BC=AQ (opposite sides of a parallelogram are equal) --------(3)

By adding the equations (1), (2) and (3) we get,

AB+AB+BC+BC+AC+AC=PB+PC+CR+AR+BQ+AQ

2AB+2BC+2AC=PQ+QR+RP

By taking common we get,

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

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