(1) A triangle is a figure made up of three line segments joining, in pairs, three non-collinear points. That is, if A, B, C are three non-collinear points, the figure formed by the three line segments AB, BC and CA is called a triangle with vertices A, B, C.
(2) The three line segments forming a triangle are called the sides of the triangle.
(3) The three sides and three angles of a triangle are together called the six parts or elements of the triangle.
(4) A triangle whose two sides are equal is called an isosceles triangle.
(5) A triangle all of whose sides are equal is called an equilateral triangle.
(6) A triangle none of whose sides are equal is called a scalene triangle.
(7) A triangle all of whose angles are acute is called an acute triangle.
(8) A triangle with one right angle is called a right triangle.
(9) A triangle with one obtuse angle is called an obtuse triangle.
(10) The interior of a triangle consists of all points P of the plane that are enclosed by the triangle.
(11) The exterior of a triangle is the part of the plane consisting of those points Q which are neither on the triangle nor in its interior.
(12) The interior of a triangle together with the triangle itself is called the triangular region.
(13) The sum of the angles of a triangle is two right angles or 180°.
(14) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.
(15) In any triangle, an exterior angle is greater than either of the interior opposite angles.
(16) The sum of any two sides of a triangle is greater than the third side.
(17) In a right triangle, if a and b are the lengths of the two shorter sides and c is the length of the hypotenuse, then c2 = a2 + b2.
(18) If the sides of a triangle are of lengths a, b and c such that c2 = a2 + b2, then the triangle is right-angled and the side of length c is the hypotenuse.
(19) Three positive integers a, b, c in this order are said to form a Pythagorean triplet if c2 = a2 + b2. Triplets (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25) and (12, 35, 37) are some common Pythagorean triplets.
