Using the Properties of Triangles

Using the Properties of Triangles

What do you already know about triangles? Triangle have three sides and three angles. Triangles are named by their vertices. The triangle in the figure below is called \(\text{Δ}ABC,\) read ‘triangle \(\text{ABC}\)’. We label each side with a lower case letter to match the upper case letter of the opposite vertex.

\(\text{Δ}ABC\) has vertices \(A,B,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}C\) and sides \(a,b,\text{and}\phantom{\rule{0.2em}{0ex}}c\text{.}\)

The three angles of a triangle are related in a special way. The sum of their measures is \(\text{180°}.\)

Example

The measures of two angles of a triangle are \(\text{55°}\) and \(\text{82°}.\) Find the measure of the third angle.

Solution

Step 1. Read the problem. Draw the figure and label it with the given information.
Step 2. Identify what you are looking for.
Step 3. Name. Choose a variable to represent it.
Step 4. Translate. Write the appropriate formula and substitute.
Step 5. Solve the equation.
Step 6. Check:
Step 7. Answer the question.

Optional Video: Animation - The Sum of the Interior Angles of a Triangle