Lesson 15Adding the Angles in a Triangle

Learning Goal

Let’s explore angles in triangles.

Learning Targets

  • If I know two of the angle measures in a triangle, I can find the third angle measure.

Lesson Terms

  • alternate interior angles
  • straight angle
  • transversal

Warm Up: Can You Draw It?

Problem 1

  1. acute
    (all angles acute)                    

    right
    (has a right angle)                  

    obtuse
    (has an obtuse angle)                

    scalene
    (side lengths all different)

    isosceles
    (at least two side lengths are equal)

    equilateral
    (three side lengths equal)

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

Activity 1: Find All Three

Problem 1

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.

Activity 2: Tear It Up

Problem 1

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?

Are you ready for more?

Problem 1

  1. Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice?

  2. Repeat this for several more quadrilaterals. Do you have a conjecture about the angles?

Lesson Summary

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

A straight line with a center point and angle measuring 180 degrees

If we experiment with angles in a triangle, we find that the sum of the measures of the three angles in each triangle is —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.

    A triangle with the angles colored red, green, and blue. These angles are cut from the triangle and attached they form a straight line.