Download 5.5 Triangle Inequality Theorem

Geometry Chapter 5: Relationships within Triangles 5.5-­‐ Use Inequalities in a Triangle SWBAT: discover the triangle inequality theorem through a hands-­‐on investigation; order side lengths and angle measures from least to greatest and vice-­‐versa. Standard: G.CO.9, G.SRT.4, G.C.3 In each baggie, there are three sets of side lengths. v The Popsicle sticks go with each other v The Blue, Red, and Green pieces of felt go together v The Orange, Yellow, and Pink pieces of felt go together Steps to complete today’s investigation: 1. Separate the side lengths according to the statements above. 2. Once separated, try moving your possible side lengths around to form a triangle. v Do your best to match up the corners of each segment in order to see if a triangle can be made. 3. Work together to answer the following questions. a) Were you able to form a triangle? Yes or No b) What did each side length measure in centimeters? Round your answers to the nearest 0.5 cm. Shortest _______________ Medium _______________ Longest _______________ c) Place the two shorter segments together, end touching end, compare the newly formed segment to the remaining segment. What do you notice? Longer, Shorter, the same d) What can you conclude? Try to write a rule regarding the lengths of the sides of a triangle and the ability to form a triangle. 4. Repeat the process for each set of side lengths. Geometry Chapter 5: Relationships within Triangles 5. Work together to answer the following questions. e) Were you able to form a triangle? Yes or No f) What did each side length measure in centimeters? Round your answers to the nearest 0.5 cm. Shortest _______________ Medium _______________ Longest _______________ g) Place the two shorter segments together, end touching end, compare the newly formed segment to the remaining segment. What do you notice? Longer, Shorter, the same h) What can you conclude? Try to write a rule regarding the lengths of the sides of a triangle and the ability to form a triangle. 6. Work together to answer the following questions. i) Were you able to form a triangle? Yes or No j) What did each side length measure in centimeters? Round your answers to the nearest 0.5 cm. Shortest _______________ Medium _______________ Longest _______________ k) Place the two shorter segments together, end touching end, compare the newly formed segment to the remaining segment. What do you notice? Longer, Shorter, the same l)
What can you conclude? Try to write a rule regarding the lengths of the sides of a triangle and the ability to form a triangle. 7. Repeat the process for each set of side lengths. Geometry Chapter 5: Relationships within Triangles Directions: Measure each angle of the three triangles below. Record your answer on the diagram to the nearest degree. Then find the length of each side of the triangles. Record your answers on the diagrams to the nearest tenth of a centimeter. Verify your results with your partner. Fill in the following tables. ∆𝑨𝑩𝑪 Largest Medium Smallest Sides Angles ∆𝑫𝑬𝑭 Largest Medium Smallest Sides Angles ∆𝑮𝑯𝑰 Largest Medium Smallest Sides Angles Geometry Chapter 5: Relationships within Triangles 1. What do you notice about the largest angles and the largest side of each triangle? 2. What do you notice about the medium angles and the medium side of each triangle? 3. What do you notice about the smallest angles and the smallest side of each triangle? Theorem 5.10 If one side of a triangle is longer than another side, then the angle opposite the longer side is _______________________ than the angle opposite the shorter side. Theorem 5.11 If one angle of a triangle is larger than antoher angle, then the side opposite the larger angle is __________________________ than the side opposite the smaller angle. Practice Problems: List the measurements of the triangles in order from least to greatest. Geometry Chapter 5: Relationships within Triangles The Triangle Inequality What do you notice about the side lengths in the diagrams above? Theorem 5.12-­‐ Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Geometry Chapter 5: Relationships within Triangles Is it possible to draw a triangle with the following side lengths? 9. 10, 13, 19 10. 25, 17, 42 Given a triangle has one side of 12 inches and another side of 18 inches. Find the range of the possible values for the third side of the triangle. Two sides of a triangle are given. Describe the possible lengths of the third side. 11. 2cm and 5cm 12. 7in. and 12in. 13. 4ft. and 12ft. 13. 6m and 17m Homework: Pgs. 331 – 333 #’s 5 – 27 Odd, 39