TRIANGLES

DISCOVERY LESSON: EXTERIOR ANGLES OF A TRIANGLE EQUAL THE SUM OF THE OPPOSITE

INTERIOR ANGLES

WARM UP1. Alternate angles are _______________________

2. Corresponding angles are ___________________________

3. Same side interior angles/co-interior angles are _____________________

4. Congruent means: ___________________________

5. Supplementary means: _________________________

6. Find the measure of angle x and y: 30 120

x y

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.

1 2

a b

c

Statements Reasons

angle 1 = angle a alternate angles are congruentangle 2 = angle b alternate angles are congruentangle 1 + angle c + angle 2 = 180 angles on a straight lineangle a + angle c + angle b = 180 substitution

Therefore the sum of the interior angles of a triangle equal 180º. 1 2

a b

c

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.

1 2

3

4

c

ba

StatementsReasons

angle 1 = aalternate angles congruentangle 2 = balternate angles congruentangle 4 = a + ccorresponding angles congruentangle 3 = angle 4vertical angles congruentangle 3 = a + csubstitutiona + c = interior opposite angles of triangleangle 3 = exterior angle of a triangleTherefore the interior opposite angles of a triangle equal the exterior angle.

c

b 3a

1 2

4

https://www.youtube.com/watch?v=yeV037nPvdc

Watch this short video explaining the exterior angle theorem.

Let’s apply what we have just proved. Always justify your reasoning.

Find the missing angles.

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.

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