Problem 28

Let ABC an isoceles triangle with AB = AC = x, BC = y. Let denote M the midpoint of AB. Find the length of CM.

Problem 27

A triangle has side lengths 15, 13 and 4 cm. Find the length of the longest altitude.

Problem 18

Given a Pythagorean triple a, b, c, prove that if a is odd, then either b or c must be odd.

Problem 17

Prove that for any m, n,  m² - n², 2mn,  and m² + n² form a Pythagorean triple.

Problem 16

Prove that there are an infinite number of Pythagorean triples.

Problem 15

Prove that if n is an odd number, then n, 0.5 (n² - 1) and 0.5 (n² + 1) form a Pythagorean triple.