The mirror operation

A point P is mirrored in the midpoints of the green triangle sides. The three mirror images form a blue triangle. Prove that it is congruent to the green one.

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The midpoints are readily seen to form a triangle similar to the green one, but scaled with a factor 1/2. The mirror operation is equivalent to a dilation of this smaller triangle from point P with a factor of 2, the net result being the congruent blue triangle.

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