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A point $P$ is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from $P$ to the sides of the triangle? Can you prove your conjecture?
If you're stuck why not try this proof sorting activity? Cut out the pieces and see if you can rearrange them into a coherent proof.
If you have Java enabled, you can experment with the interactive diagram below by clicking and dragging the red points