1. 1.Get out a pencil and 2 pieces of paper. 2.Start working on your warm-ups. SILENTLY (that means without talking)…

2. Learning Target: Students can find unknown angles in triangles. Math 8 Day 17

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

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

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

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

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

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

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

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

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

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

13. 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.

14. 62° + t° + t° = 180° 62° + 2t° = 180° 2t° = 118° –62° –62° Find the angle measures in the isosceles triangle. 2t° = 118° 2 t° = 59° Triangle Sum Theorem Combine like terms. Subtract 62° from both sides. Divide both sides by 2. The angles labeled t° measure 59°. Example 7:

15. 2x° + 3x° + 5x° = 180° 10x° = 180° x = 18° 10 10 Find the angle measures in the scalene triangle. Triangle Sum Theorem Combine like terms. Divide both sides by 10. 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°. Example 8:

16. 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°.