draw a triangle ABC and three altitudes
AH
BL
and CM
AH_|_ BC
BL _|_AC
and CM _|_ AB
for right triangle AHB, using Pythagorean
AH² = AB² - BH²
so AH < AB
similarly for other altitudes
thus
AH+BL+CM is < AB+BC+CA
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an isisceles triangle is a triangle with atleast two sides congruent.
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== ==
The shortest path between two points is a straight line. This is a mathematical fact, which can be proven in another question.The diagonal of a quadrilateral is a straight line between two opposing (non-adjacent) vertices. The perimeter of a quadrilateral will include two separate paths between the same vertices. The difference is that these two paths are each composed of two linked line segments, so each of these paths will be longer than the diagonal.Therefore, the length of the perimeter of a quadrilateral will be greater than twice the length of either diagonal.
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