1. Pretest Please complete the pretest for this standard on your own. Try to remember all you can from our first discussion of this topic.

2. Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem. MA.912.G.4.7

3. LEQ: How do I apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem? Property/Corollary/TheoremDefinition Comparison Property of Inequality Corollary to the Triangle Exterior Angle Theorem Theorem 5-10 Theorem 5-11 If a = b + c and c > 0 then a > b The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.

4. Property/Corollary/TheoremDefinition Triangle Inequality Theorem The Hinge Theorem (SAS Inequality Theorem) Converse of the Hinge Theorem (SSS Inequality) LEQ: How do I apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle. If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larder included angle is opposite the longer third side.

5. I do… Which of the following are not possible sides for a triangle? a.1 yd, 1yd, 3 ydc.3 in, 6 in, 8 in b.10 cm, 12 cm, 20 cmd.14 mm, 14 mm, 25 mm Since 1+1 is not greater than 3, choice “a” cannot form a triangle.

6. I do… Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 158 ft from camera 2, which was 121 ft from camera 3. Cameras 1 and 3 were 140 ft apart. Which camera had to cover the greatest angle? Camera 2 Camera 3Camera 1 158 ft121 ft 140 ft By the converse of the Hinge Theorem, since the length across from camera 3 is the greatest, camera 3 has the biggest angle.

7. Sage and Scribe We do…

8. District School Board Pasco County With your shoulder partner, identify the error(s) in planning the solution or solving the problem. Then write the correct solution.

9. You do… 1.Two sides of a triangle have lengths of 7 and 11. Which of the following cannot be the length of the third side? A. 11 B. 13 C. 15 D. 19 2.Kristin has two dogs, Buddy and Socks. She stands at point K in the diagram and throws two disks. Buddy catches one at point B, which is 11 meters (m) from Kristin. Socks catches the other at point S, which is 6 m from Kristin. If KSB forms a triangle, which could be the length, in meters, of segment SB? A.5 m B. 8 m C. 17 m D. 22 m 3. A surveyor took some measurements across a river, as shown below. In the diagram, AC = DF and AB = DE. The surveyor determined that measure of angle BAC = 29 and the measure of angle EDF = 32. Which of the following can he conclude? A. BC > EF B. BC < EF C. AC > DE D. AC < DF

10. 1.Two sides of a triangle have lengths of 7 and 11. Which of the following cannot be the length of the third side? A. 11 B. 13 C. 15 D. 19 You do…

11. 2.Kristin has two dogs, Buddy and Socks. She stands at point K in the diagram and throws two disks. Buddy catches one at point B, which is 11 meters (m) from Kristin. Socks catches the other at point S, which is 6 m from Kristin. If KSB forms a triangle, which could be the length, in meters, of segment SB? A.5 m B. 8 m C. 17 m D. 22 m You do…

12. 3. A surveyor took some measurements across a river, as shown below. In the diagram, AC = DF and AB = DE. The surveyor determined that measure of angle BAC = 29 and the measure of angle EDF = 32. Which of the following can he conclude? A. BC > EF B. BC < EF C. AC > DE D. AC < DF You do…

13. Post Test Please complete the post test for this standard on your own. Do the best you can, hopefully you will show improvement over your pretest score.