Get out a pencil and 2 pieces of paper. SILENTLY (that means without talking)… Get out a pencil and 2 pieces of paper. Start working on your warm-ups. When finished with warm-ups, get one of your pieces of paper and title it “Interior Angles Notes.” Don’t do anything with the other piece of paper. Do not touch the scissors when they are passed out.

Learn Target: Students can find unknown angles in triangles. Math 8 Day 14 Learn Target: Students can find unknown angles in triangles.

Vocabulary Triangle Sum Theorem acute triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

Cut a triangle out of your paper. Tear off two corners of the triangle and place them next to the third corner. What do you notice about the three angles? What do they form?

Draw a triangle and extend the bottom side Draw a triangle and extend the bottom side. Then draw a line parallel to the extended side, as shown. The sides of the triangle are transversals to the parallel lines. The three angles in the triangle can be arranged to form a straight line or 180°.

An acute triangle has 3 acute angles An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

Example 1: Find p° in the acute triangle. 73° + 44° + p° = 180° 117° + p° = 180° –117° –117° p° = 63°

Example 2: Find c° in the right triangle. 42° + 90° + c° = 180° 132° + c° = 180° –132° –132° c° = 48°

Example 3: Find m° in the obtuse triangle. 23° + 62° + m° = 180° 85° + m° = 180° –85° –85° m° = 95°

Example 4: Find a° in the acute triangle. 88° + 38° + a° = 180° 38° 126° + a° = 180° –126° –126° a° = 54° a° 88°

Example 5: Find b in the right triangle. 38° 38° + 90° + b° = 180° 128° + b° = 180° –128° –128° b° = 52° b°

Example 6: Find c° in the obtuse triangle. 24° + 38° + c° = 180° 38° 62° + c° = 180° 24° c° –62° –62° c° = 118°

Interior Angles Theorem: The sum of the interior angles of a triangle is ________°

An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

Example 7: Find the angle measures in the isosceles triangle. 62° + t° + t° = 180° Triangle Sum Theorem 62° + 2t° = 180° Combine like terms. –62° –62° Subtract 62° from both sides. 2t° = 118° 2t° = 118° 2 2 Divide both sides by 2. t° = 59° The angles labeled t° measure 59°.

Find the angle measures in the scalene triangle. Example 8: Find the angle measures in the scalene triangle. 2x° + 3x° + 5x° = 180° Triangle Sum Theorem 10x° = 180° Combine like terms. 10 10 Divide both sides by 10. x = 18° The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

Ticket Out the Door 1. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°. 2. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°.