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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.
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