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
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)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.
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The measurement of one of the angles is labeled. Mentally estimate the measures of the other two angles.
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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.
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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
Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice?
Repeat this for several more quadrilaterals. Do you have a conjecture about the angles?
Lesson Summary
A
If we experiment with angles in a triangle, we find that the sum of the measures of the three angles in each triangle is
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.