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Transcript

Triangle Inequalities What makes a triangle and what type of triangle What makes a triangle How do we know if the side lengths given could be used to construct or draw a triangle Pg 216 Investigation 1 The sum of the lengths of the two shorter sides should be greater than the length of the longest side. Examples Given sides do they make a triangle 3 5 8 No 3+5=8 3 5 9 No 3+5 <9 3 5 7 Yes 3+5>7 Angle and Side Relationship How can you determine what side is the longest given the angles or what angle is the largest given the sides Pg 217 Investigation 2 The longest sides is across from the largest angle The largest angle is across from the longest side Smallest angle across from shortest side Shortest side across from the smallest angle Example Put sides in order from Longest to shortest c 70 a 60 b,a,c 50 b Put angles in order from largest to smallest 6 c a 8 b 10 c,a,b Exterior Angle of A triangle What relationship do you notice about the exterior angle of a triangle in relationship to the interior angles Pg 217 investigation 3 The exterior angle is equal to the sum of the two remote interior angles Remote interior angles are the two angles not adjacent to the exterior angle Example Find the missing angle x X=60 115 55 X=120 55 65 x How can the sides determine the type of Triangle How do we know if a triangle is a right triangle? Pythagorean’s Theorem – a 2 b 2 c 2 where a and b are the shortest 2 sides and c is the longest 2 2 2 Obtuse a b c Acute a b c 2 2 2 Examples 4 6 8 Obtuse 16+36<64 5 8 9 Acute 25+64>81 6 8 10 Right 36+64=100 Homework Pg 218 1-4 do the sides make a triangle and what kind 5,6,9,10,12,15,16 Honors 17