1. Geometry 5-5 Inequalities in Triangles Within a triangle: – the biggest side is opposite the biggest angle. – the smallest side is opposite the smallest angle. A B C SmallestBiggest BC AB AC ∠ A ∠ C ∠ B 12 5 9

2. Examples List the sides from shortest to longest. List the angles from largest to smallest. A B C 55° 62° 63° DF = 23 DE = 14 EF = 12

3. Constructing Triangles The two shortest sides of a triangle must add up to be greater than the third side. 7 4 3 4 +4 > 7 Can make a Δ 3 +3 > 7 Cannot make a Δ 4 +3 > 7 Cannot make a Δ

4. Example Can the following sets of numbers be the sides of a triangle? 19, 10, 7 21, 8, 13 7, 9, 6.2

5. Example Find the range of values that could be the third side of a triangle. Given: 6 and 15Given: 40 and 11