Pembuktian Teorema Menelaus

Dipunyai segitiga ABC seperti tampak pada gambar di bawah ini!

Sebuah garis melintas membagi segitiga tersebut menjadi 2 bangun, memotong sisi segitiga dan perpanjangannya di P, Q, dan R.

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Penyelesaian!
Draw segment a, b, and c, such that a // b // c. Line a pass through vertex A, line b pass through vertex B, and also line c. See figure below!

Proofing of Menelaus theorem

Look at triangle PAK and triangle PBM!
Obvious triangle PAK ≈ triangle PBM (Why?). So that we get
Because P doesn’t lie between A and B, then we get

Look at triangle QBM and triangle QCL!
Obvious triangle QBM ≈ triangle QCL (Why?) So that we get

Because Q lies between B and C, then we get

Look at triangle RAK and triangle RLC!
Obvious triangle RAK ≈ triangle RLC (Why?) So that we get

Because R lies between C and A, then we get

Thus, from three equations above we get

This proves Menelaus theorem

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Pembuktian Teorema Menelaus

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Oleh Wahyu Eko Nugroho

Ditulis Wahyu Eko Nugroho Pada Friday, March 21, 2014 Komentar