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Warm -up

1. 2. 60. 4x. 2x. x. X+15. Warm -up. Copy the pictures, find x and the measure of each angle. 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

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Warm -up

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  1. 1. 2. 60 4x 2x x X+15 Warm -up • Copy the pictures, find x and the measure of each angle. 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. • 2 cm, 5 cm, 8 cm • 7 in, 5 in, 3 in • 20 m, 7 m, 13m • 16 cm, 30 cm, 45 cm • 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. 55° 30° b c f d 68° 57° 60° a e c, b, a f, d, e

  7. Example #3 • Arrange the unknown measures in order from greatest to least. a. b. c 87° 32° a b b 61° 13 18 a c b, c, a 20 b, a, c

  8. EXTERIOR ANGLE ADJACENT INTERIOR ANGLE REMOTE INTERIOR ANGLES 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.

  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. 135° x 40° 120° x x x + 40° = 120° x = 80° x + x = 135° 2x = 135° x = 67.5°

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

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

  13. Homework • Pg 216 # 1-16

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