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

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Presentation on theme: "TRIANGLES DISCOVERY LESSON: EXTERIOR ANGLES OF A TRIANGLE EQUAL THE SUM OF THE OPPOSITE INTERIOR ANGLES."— Presentation transcript:

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.

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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.

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