Entry Task In Webgeogebra.org construct a triangle. Carefully measure each side and angle in each triangle. List the sides of the triangle in order from longest to shortest. List the angles of each triangle from largest to smallest. What do you notice about the relationship between the longest side and the largest angle? What about the shortest side and the smallest angle? If you drag a vertex around, does it change this releationship?

Section 5-5 Inequalities in Triangles GEOMETRY 11/06/15

Theorem If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side (and the smaller angle lies opposite the shorter side). EX: if XZ > XY, then m ∡Y > m∡Z X Y Z

Theorem – Conversely… If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle (and the shorter side lies opposite the smaller angle). EX: if m ∡Y > m∡Z, then XZ > XY X Y Z

Let’s Practice Write the sides of the following triangles in order from longest to shortest: X Y Z 57⁰ 64⁰

Let’s Practice Write the sides of the following triangles in order from longest to shortest: X Y Z 60⁰ 36⁰

Let’s Practice Write the angles of the following triangle in order from largest to smallest: X Y Z10 cm 5.5 cm 8 cm

Sides of a Triangle Can a triangle be formed from any three side lengths? Write your answer in your notebook

Spaghetti Triangles Break one piece of spaghetti into three pieces and create a triangle.

Spaghetti Triangles Did it work? If it did not, use your second piece of spaghetti to create a side lengths that will work. If it did work, use your second piece of spaghetti to create side lengths that do not work.

Spaghetti Triangles What do you notice about the relationship between the side lengths for the triangle that did work, versus the triangle that did not work? Within your group try to make a conjecture about the relationship between the side lengths of a triangle.

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. XY + YZ > XZ XZ+XY > YZ YZ + XZ > YX X Y Z

Let’s Practice Write whether the following could be possible sides of a triangle: 3 ft, 7 ft, 8 ft 3 in, 10 in, 6 in 7cm, 12cm, 19cm

Let’s Practice A triangle has side lengths of 8 cm and 10 cm. What are the possible side lengths for the 3 rd side? Write the answer on your white board.

Homework Pg 328; problems 1-4, 9, 16, 28, 30, 37