Word problem #1 Your family is considering moving to a new home. You want to be equidistant from the school, from your mom’s work and your dad’s work. These 3 places form a triangle. Draw a diagram and tell how you would find the best place to live. What is this point called?

Agenda Notes on Inequalities in Triangle Worksheet HW – Workbook Pg 299 #1-8, 11-18

Table of Contents Inequalities in a Triangle

5.1 Inequalities in a Triangle Essential Question – How can you determine which side is the longest or shortest in a triangle?

In a Δ the longest side is opposite the largest angle, the shortest side is opposite the smallest angle. Ex: List the sides in order from shortest to longest. Seg AC, seg AB, seg BC A B C 115 o 25 o 40 o

Example: list the angles in order from biggest to smallest  Z,  X,  Y X Y Z 8 5 6

Triangle inequality theorem The sum of the lengths of any 2 sides of a Δ is greater than the length of the 3 rd side. XY+YZ>XZ XY+XZ>YZ YZ+XZ>XY Y X Z

Example: Is it possible for a Δ to have side lengths of the following? a) 10cm, 12 cm, 3cm 10+12>3 10+3> >10 b) 14ft, 22ft, 6ft 14+22>6 14+6> >14 c) 15in, 10 in, 5in 5+15> >5 10+5>15

Example: A Δ has side lengths of 12 and 15 cm. What are the possible lengths for the 3 rd side? Side lengths: 12, 15, x x < OR x < 27 x > OR x > 3 3<x<

Exterior-Angle Inequaltiy Theorem The measure of an ext. angle of a triangle is greater than either of the non-adjacent interior angles. (Remote interior angles) Angle 4>angle 2 Angle 4>angle 1 In fact ang 4=ang 1 +ang 2

Assignment Workbook Pg and 11-18

Assessment Answer the essential Question: How can you determine which side is longest or shortest in a triangle?