Applications

We see triangles frequently in nature. What naturally occurring triangles have you seen lately? A triangular shape allows many conifers to effectively shed snow and triangles provide excellent force distribution as seen in the design of trusses and bridges.

What Makes a Triangle?

If you connect three line segments into a polygon – you’ve got a triangle! Three sides and three angles define this shape. The interior angles of all triangles add to 180°. We often use this property to find the measure of a missing angle.

(On a related tangent… Sometimes we use the term supplementary to describe two angles that add to 180 ° and the term complementary to describe two angles that add to 90 °.)

Classifying Triangles

We can classify triangles into three categories based on the lengths of their sides.

• Equilateral triangle: all three sides have the same length
• Isosceles triangle: exactly two sides have the same length
• Scalene triangle: all three sides have different lengths

We can also classify triangles into three categories based on the measures of their angles.

• Obtuse triangle: one of the angles is an obtuse angle
• Right triangle: one of the angles is a right angle
• Acute triangle: all three of the angles are acute

Relationships Among Sides and Angles

We use specific terms to refer to the sides and angles of a triangle and their relationship to one another. The side of a triangle directly across from an angle is called opposite with respect to that angle. Another way to see this is that this opposite side is not one of the lines that forms the angle. If a side is one of the lines that forms the angle, it is referred to as adjacent to that angle. In a right triangle, the side opposite of the 90 deg angle is called the hypotenuse. It is the longest side of the triangle because it is opposite the largest angle.