2.  When the sides of a polygon are extended, other angles are formed.  The original angles are the interior angles.  The angles that form linear pairs with the interior angles are the exterior angles. Angles

3. An exterior angle of a triangle… … is equal in measure to the sum of the measures of its two remote interior angles. remote interior angles Exterior angle

4. The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles 3 2 1 4 exterior angle remote interior angles m<1 + m<2 = m<4

5. m ∠ 1 = m ∠ A + m ∠ B

6. m<G = 60 + 69 m<FHG = 180 – 111 = 69 linear pair

7. x 82° 30° y Find x & y x = 68° y = 112° y = 30 + 82 y = 112˚ 180 = 30 + 82 + x 180 = 112 + x 68˚ = x

8. Find 2x – 5 = x + 70 x – 5 = 70 x = 75 m< JKM = 2(75) - 5 m< JKM = 150 - 5 m< JKM = 145˚

9. Solve for y in the diagram. Solve on your own before viewing the Solution

10. 4y + 35 = 56 + y 3y + 35 = 56 3y = 21 y= 27

11. Find the measure of in the diagram shown. Solve on your own before viewing the Solution

12. 40 + 3x = 5x - 10 40 = 2x - 10 50 = 2x 25 = x m < 1= 5x - 10 m < 1= 5(25) - 10 m < 1= 125 - 10 m < 1= 115

14. Right Scalene triangle x + 70 = 3x + 10 70 = 2x + 10 60 = 2x 30 = x 3 (30) + 10 = 100˚

16. Make A Triangle Construct triangle DEF. DF FE DE

17. DF FE DE Make A Triangle Construct triangle DEF.

18. DE Make A Triangle Construct triangle DEF.

19. DE Make A Triangle Construct triangle DEF.

20. DE Make A Triangle Construct triangle DEF.

21. DE 53 13 Q:What’s the problem with this? A:The shorter segments can’t reach each other to complete the triangle. They don’t add up. Make A Triangle Construct triangle DEF.

22. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Triangle Inequality Conjecture Add the two smallest sides; they MUST be larger than the third side for the triangle to be formed.

23. Make A Triangle Can the following lengths form a triangle? 1. 4 mm 5 mm 10 mm 2. 2 ft 9 ft 13 ft 5. 10 mm 3 mm 6 mm 8. 8 m 7 m 1 m 9. 9 mm 2 mm 1 mm 12. 1 mm 5 mm 3 mm 3. 5 cm cm 4 cm 4. 7 ft 15 ft ft 6. 7 ft ft 7. 10 mm 13 mm mm 10. 12 mm 22 mm mm 11. 7 mm 8 mm mm

24. In a triangle, if one side is longer than another side, then angle opposite the longer side is larger than the other. Side-Angle Conjecture

25. Side-Angle What’s the biggest side? What’s the biggest angle? What’s the smallest side? What’s the smallest angle? C B A b a c b B a A

26. Side-Angle 92° 42° 46° a b c Rank the sides from greatest to least. b c a Rank the angles from greatest to least. C A B A C B 7 5 4