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MathNet 2008-part-04 — 165 problems (EN–VI) Question 139

Math Olympiad Vault · MathNet 2008-part-04 — 165 problems (EN–VI)

Question 139

A triangle (with non-zero area) is constructed with the lengths of the sides chosen from the set
$$
\{2, 3, 5, 8, 13, 21, 34, 55, 89, 144\}
$$
Show that this triangle must be isosceles. (A triangle is isosceles if it has at least two sides the same length.)