5.5 Inequalities in One Triangle

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Presentation transcript:

5.5 Inequalities in One Triangle

Order of sides in a triangle The largest side of a triangle is across from the largest angle; the smallest side is across from the smallest angle.

Conversely The largest angle of a triangle is across from the largest side; the smallest angle is across from the smallest side.

Another Theorem about Inequalities Remember that an exterior angle is the sum of the remote interior angles, then the next theorem should not be surprising. An outside angle is greater then either of the remote interior angles.

Christmas wrapping principle When wrapping a flat object, you need to have enough paper to make a triangle over the top. The sum of any two sides of a triangle is greater then the third side.

Write the angles in order then the sides

Write the sides in order then the angles

Can these sides be sides of a triangle? #1. 3, 3, 8 #2. 6, 6, 12 #3. 9, 5, 11

What is the possible values for the last side? A triangle have one side of 8 and another of 17, what are the possible of the third side. Greater then But Less then

Homework Page 298 # 6 - 23

Homework Page 299 – 301 # 24 – 31, 42 - 45