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Warm -up Copy the pictures, find x and the measure of each angle. 1. 2. 60 2x 4x x X+15 Front reflection: If 2 triangles have all corresponding angles congruent are the triangles congruent? Explain 4.3 Triangle Inequalities Year 2 Geometry Materials: Patty paper Ruler & protractor Chapter 4.3 in your book. 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 GREATER THAN of a triangle must be _______________ the length of the third side. Example #1 a. b. c. d. e. Determine whether it is possible to draw a triangle with the given sides. State the reason. NO, 2 + 5 < 8 2 cm, 5 cm, 8 cm YES, 3 + 5 > 7 7 in, 5 in, 3 in NO, 7 + 13 = 20 20 m, 7 m, 13m YES, 16 + 30 > 45 16 cm, 30 cm, 45 cm NO, 9 + 17 < 28 9 km, 17 km, 28 km 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 LARGER THAN THE ANGLE OPPOSITE THE SHORTER SIDE is _________________________________. Example #2 Arrange the unknown measures in order from greatest to least. a. b. 55° b 30° c f d 68° 57° 60° a e c, b, a f, d, e Example #3 Arrange the unknown measures in order from greatest to least. a. b. c 87° a b 13 c 20 b, a, c b 61° 18 a 32° b, c, a 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 REMOTE INTERIOR ANGLES ADJACENT INTERIOR ANGLE 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. ___________________________________. Example #4 Find the missing value. a. b. 135° x 40° 120° x x + 40° = 120° x = 80° x + x = 135° 2x = 135° x = 67.5° x Example #5 Find m<E a. Find the missing value. 10x+4 b. 4x+5 x+15 68 23x-6° 70° 23x-6 = 68+10x+4 4x+5+x+15 = 70 5x+20=70 5x = 50 X = 10 23x-6=10x+72 13x – 6 = 72 13x = 78 x =6 <E = 10(6) +4 = 64 E Summary Write a three complete sentences about three main ideas from today. Homework Pg 216 # 1-16