Ordering Sides and Angles in Triangles

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

The sum of the interior angles in a triangle is always 180 degrees.

To order angles from smallest to largest, compare their measures. The angle with the smallest measure is first, followed by the next smallest, and so on.

A triangle is a polygon with three edges and three vertices.

1. Equilateral Triangle: All sides are equal. 2. Isosceles Triangle: Two sides are equal. 3. Scalene Triangle: All sides are different.

1. Acute Triangle: All angles are less than 90 degrees. 2. Right Triangle: One angle is exactly 90 degrees. 3. Obtuse Triangle: One angle is greater than 90 degrees.

You can use the Law of Sines or the Law of Cosines to find the length of a side when you know the angles and other sides.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides: a/sin(A) = b/sin(B) = c/sin(C).

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab*cos(C).

An exterior angle is formed by one side of the triangle and the extension of an adjacent side. The measure of an exterior angle is equal to the sum of the two opposite interior angles.