Ordering Sides and Angles in Triangles

Front

What is the relationship between the angles and sides in a triangle?

Back

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

Front

What is the sum of the angles in a triangle?

Back

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

Front

How do you order angles in a triangle from smallest to largest?

Back

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.

Front

What is the definition of a triangle?

Back

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

Front

What are the types of triangles based on side lengths?

Back

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

Front

What are the types of triangles based on angles?

Back

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.

Front

How do you find the length of a side in a triangle using angles?

Back

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.

Front

What is the Law of Sines?

Back

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).

Front

What is the Law of Cosines?

Back

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).

Front

What is an exterior angle of a triangle?

Back

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.