1. TRIANGLES
DISCOVERY LESSON: EXTERIOR ANGLES OF A TRIANGLE EQUAL THE SUM OF THE OPPOSITE INTERIOR ANGLES

2. WARM UP 120 x y Alternate angles are _______________________
Corresponding angles are ___________________________
Same side interior angles/co-interior angles are _____________________
Congruent means: ___________________________
Supplementary means: _________________________
Find the measure of angle x and y:
120
x y

3. Today we are going to prove that the exterior angle of a triangle is equal to the sum of opposite interior angles. Before we can do that, we must prove that the sum of the angles of a triangle equals 180º.
Spend a few minutes in your groups trying to prove the
theorem that states that the angles of a triangle equal 180º.
Use your prior knowledge of lines and parallel lines to help you. a b c

4. Statements Reasons angle 1 = angle a alternate angles are congruent
angle 2 = angle b alternate angles are congruent
angle 1 + angle c + angle 2 = 180 angles on a straight line
angle a + angle c + angle b = 180 substitution
Therefore the sum of the interior angles of a triangle equal 180º. a b c

5. Now, using parallel lines, and what you have just proved, prove that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. 3 4 c b a

6. Statements Reasons angle 1 = a alternate angles congruent
angle 2 = b alternate angles congruent
angle 4 = a + c corresponding angles congruent
angle 3 = angle vertical angles congruent
angle 3 = a + c substitution
a + c = interior opposite angles of triangle
angle 3 = exterior angle of a triangle
Therefore the interior opposite angles of a triangle equal the
exterior angle. c
b 3 a 1 2 4

7. Watch this short video explaining the exterior angle theorem.

8. Let’s apply what we have just proved. Always justify your reasoning.
Find the missing angles.

10. Time to reflect…..
Take a few minutes to think about what you have learned today. Write a short paragraph explaining why the exterior angle of a triangle is equal to the opposite interior angles. Use the diagram to help you.

11. Complete the following worksheet. You may work with a partner.