1. Warm -up Copy the pictures, find x and the measure of each angle. 2xx 60 1. 4x X+15 2. Front reflection: If 2 triangles have all corresponding angles congruent are the triangles congruent? Explain

2. 4.3 Triangle Inequalities Year 2 Geometry Materials:  Patty paper  Ruler & protractor  Chapter 4.3 in your book.

3. Investigation #1 Follow the directions in the book pg. 214 Use patty paper to trace the lines. Triangle Inequality Conjecture The sum of the lengths of the two shorter sides of a triangle must be _______________ the length of the third side. GREATER THAN

4. Example #1 Determine whether it is possible to draw a triangle with the given sides. State the reason. a. 2 cm, 5 cm, 8 cm b. 7 in, 5 in, 3 in c. 20 m, 7 m, 13m d. 16 cm, 30 cm, 45 cm e. 9 km, 17 km, 28 km NO, 2 + 5 < 8 YES, 3 + 5 > 7 NO, 7 + 13 = 20 YES, 16 + 30 > 45 NO, 9 + 17 < 28

5. Investigation #2 Follow the directions in the book pg. 215 Side-Angle Inequality Conjecture In a triangle, if one side is longer than another side, then the angle opposite the longer side is _________________________________. LARGER THAN THE ANGLE OPPOSITE THE SHORTER SIDE

6. Example #2 Arrange the unknown measures in order from greatest to least. a.b. a c b 68° 55° 60° f e d 57° c, b, a 30° f, d, e

7. Example #3 Arrange the unknown measures in order from greatest to least. a.b. a b c 20 1813 c b a 32° 61° b, a, c 87° b, c, a

8. Exterior Angles of a Triangle Triangle also have exterior angles. If you extend one side of a triangle beyond its vertex, then you have constructed an exterior angle at that vertex. EXTERIOR ANGLE ADJACENT INTERIOR ANGLE REMOTE INTERIOR ANGLES

9. Investigation #3 Follow the directions in the book pg. 215-216 Use patty paper to trace the angles. Triangle Exterior Angle Conjecture The measure of an exterior angle of a triangle ____________________________________ ___________________________________. IS EQUAL TO THE SUM OF THE MEASURES OF THE REMOTE INTERIOR ANGLES.

10. Example #4 Find the missing value. a.b. 120°40° x x x + 40° = 120° x = 80° 135° x x + x = 135° 2x = 135° x = 67.5°

11. Example #5 Find the missing value. a.b. 70° x+15 4x+5 4x+5+x+15 = 70 5x+20=70 5x = 50 X = 10 23x-6 = 68+10x+4 23x-6=10x+72 13x – 6 = 72 13x = 78 x =6 23x-6° 10x+468 Find m<E E <E = 10(6) +4 = 64

12. Summary Write a three complete sentences about three main ideas from today.

13. Homework Pg 216 # 1-16