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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 Y X 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 Y X Z Let’s Practice • Write the sides of the following triangles in order from longest to shortest: Y X 57⁰ 64⁰ Z Let’s Practice • Write the sides of the following triangles in order from longest to shortest: Y X 60⁰ 36⁰ Z Let’s Practice • Write the angles of the following triangle in order from largest to smallest: Y X 10 cm Z 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 Y X 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 3rd side? • Write the answer on your white board. Homework Pg 328; problems 1-4, 9, 16, 28, 30, 37