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 trianglePg 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 8No 3+5=83 5 9No 3+5 <93 5 7Yes 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 sidesPg 217 Investigation 2The longest sides is across from the largest angleThe largest angle is across from the longest sideSmallest angle across from shortest sideShortest side across from the smallest angle

Example

Put sides in order from Longest to shortest

Put angles in order from largest to smallest

c

b

a70

6050

10

86

c

ba

b,a,c

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 anglesPg 217 investigation 3The exterior angle is equal to the sum of the two remote interior anglesRemote interior angles are the two angles not adjacent to the exterior angle

Example

Find the missing angle

55 115

x X=60

65

55

x

X=120

How can the sides determine the type of Triangle

How do we know if a triangle is a right triangle?Pythagorean’s Theorem –

where a and b are the shortest 2 sides and c is the longest

Obtuse

Acute

222 cba

222 cba

222 cba

Examples

4 6 8Obtuse 16+36<64

5 8 9Acute 25+64>81

6 8 10Right 36+64=100

Homework

Pg 218 1-4 do the sides make a triangle and what kind5,6,9,10,12,15,16Honors 17