Geometry · Foundation · 5 min
Triangle angle sum
A triangle can change shape while its three interior angles keep the same total.
WHAT HAPPENS IF…Can moving the apex outside the base change the total?
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Draw a line through the apex parallel to the base. Alternate interior angles reproduce the two base angles at the apex. Those two angles and the apex angle form a straight angle, π radians. The display restricts the height to be positive so the triangle never collapses.
A detail that matters
This theorem concerns a nondegenerate triangle in a flat Euclidean plane.
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