Lesson 15: Adding the Angles in a Triangle

Let’s explore angles in triangles.

15.1: Can You Draw It?

  1. Complete the table by drawing a triangle in each cell that has the properties listed for its column and row. If you think you cannot draw a triangle with those properties, write “impossible” in the cell.

  2. Share your drawings with a partner. Discuss your thinking. If you disagree, work to reach an agreement.

    acute (all angles acute) right (has a right angle) obtuse (has an obtuse angle)
row 1 scalene (side lengths all different)      
row 2 isosceles (at least two side lengths are equal)      
row 3 equilateral (three side lengths equal)      

15.2: Find All Three

Your teacher will give you a card with a picture of a triangle.

  1. The measurement of one of the angles is labeled. Mentally estimate the measures of the other two angles.

  2. Find two other students with triangles congruent to yours but with a different angle labeled. Confirm that the triangles are congruent, that each card has a different angle labeled, and that the angle measures make sense.

  3. Enter the three angle measures for your triangle on the table your teacher has posted.

15.3: Tear It Up

Your teacher will give you a page with three sets of angles and a blank space. Cut out each set of three angles. Can you make a triangle from each set that has these same three angles?

Summary

A $180^\circ$ angle is called a straight angle because when it is made with two rays, they point in opposite directions and form a straight line.

If we experiment with angles in a triangle, we find that the sum of the measures of the three angles in each triangle is $180^\circ$—the same as a straight angle!

Through experimentation we find:

  • If we add the three angles of a triangle physically by cutting them off and lining up the vertices and sides, then the three angles form a straight angle.

  • If we have a line and two rays that form three angles added to make a straight angle, then there is a triangle with these three angles.

Practice Problems ▶

Glossary

straight angle

straight angle

 If the two rays that make an angle form a straight line, we call the angle a straight angle.