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In any right triangle with legs a and b and hypotenuse c, the Pythagorean theorem states that a2 + b2 = c2. Common integer Pythagorean triples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).
For any convex polygon with n sides, the sum of all interior angles is given by (n - 2) × 180 degrees. In a regular polygon, all interior angles are equal, each measuring ((n - 2) × 180) / n degrees.
Pythagorean Theorem
a2 + b2 = c2
Valid strictly for right triangles
Polygon Interior Angles
Sum = (n - 2) × 180 degrees
Hexagon (n=6) sums to 4 × 180 = 720 degrees
Isosceles Right Triangle
Legs x, hypotenuse x × √(2)
Angles are 45, 45, and 90 degrees
30-60-90 Triangle
Sides in ratio 1 : √(3) : 2
Shortest leg opposite 30 degree angle
Esempio svolto
1.The sum of the interior angles of a convex hexagon (6 sides) is 720 degrees.
2.A right triangle with legs 3 cm and 4 cm has a hypotenuse of 5 cm.
3.In an isosceles right triangle with leg length 6 cm, the hypotenuse is 12 cm.
Accesso a vita a tutte le 7 lezioni di Mathematics, mappe concettuali interattive, quesiti risolti passo per passo e simulazioni d'esame a tempo per CEnT-S.