Triangle

in plane geometry, a figure bounded by three straight lines and having consequently three angles. A triangle having two or more equal sides is said to be isosceles. A triangle having a right angle is known as a right-angled triangle. The side opposite the right angle is called the hypotenuse. The side on which a triangle is supposed to rest is called the base. The angle opposite the base is known as the vertex. The altitude of a triangle is the perpendicular distance from the vertex to the base. The area of a triangle may be found by taking one-half the product of the base and altitude. According to one of the most famous propositions of geometry, the square on the hypotenuse of a rightangled triangle is equal to the sum of the squares of the other two sides. No change can be made in the magnitude of an angle of a triangle without changing the length of one side. Carpenters and builders take advantage of this principle in bracing buildings. A brace nailed or mortised across a joint so as to form a triangle prevents the frame of a building from swaying.