In this activity, you and a partner will examine whether there are any restrictions regarding the possible side lengths of triangles. You will need: 3 Twizzlers 3 pretzel sticks 3 pretzel rods 2 pieces of spaghetti I. First, measure each of your items in inches. Round to the nearest 1/16 of an inch. Twizzler: ____________ Pretzel Rod:____________ Pretzel Stick:____________ Spaghetti:____________ Measurement II.Now you are going to construct various triangles. Directions: 1) After you create the triangle, draw your creation in the box provided. Be sure to label the sides with appropriate measurements. 2) If you cannot construct the triangle that is described, please indicate that result. 3) Finally, list the numerical side lengths at the bottom of the box. 1) 3 Twizzlers2) 2 Twizzlers; 1 Spaghetti3) 1 Twizzler, 2 Pretzel Sticks 4) 2 Pretzel Rods, 1 Pretzel Stick 5) 1 Pretzel Rod, 1 Pretzel Stick, 1 Spaghetti 6) 1 Pretzel Stick, 1 Twizzler, 1 Spaghetti Sides: ____, ____, ____ Geometry/Trig 2 Name __________________________ 6-4 Triangle Inequality NotesDate ___________________________

Conclusions: 1.List the side lengths of the triangles you could create.__________________________________________________ 2.List the side lengths of the triangles you could NOT create.__________________________________________________ 3. Based on these lists, what do you think the rule is regarding creating triangles? [Hint: Think about the Segment Addition Postulate] Theorem: If one side of a triangle is longer than a second side, ______________________ ______________________________________________________________________ Diagram: Geometry/Trig Triangle Inequality Notes Page 2 _______________________________________________ A C B Example 1: _____________ Example 2: _____________ Example 3: _____________ List the angles of each triangle in order from largest to smallest. D E F I H G

Theorem: If one angle of a triangle is larger than a second angle, ____________________ ______________________________________________________________________ Diagram: _______________________________________________ A C B Example 4: _____________ Example 5: _____________ Example 6: _____________ List the sides of each triangle in order from shortest to longest. DE F IH G Theorem: The Triangle Inequality ___________________________________________ ______________________________________________________________________ Example 7: Example 8: Example 9: Example 10: Can a triangle have the given sides? The lengths of the two sides of a triangle are given. Describe, as an inequality, the lengths possible for the third side. Example 11: Example 12: Example 13: Geometry/Trig Triangle Inequality Notes Page 3