Honors Geometry Warm-up: Sketch an angle bisector. Today: 5.5 HW ???? 5.6 Instruction TEST MONDAY! 5.6 there is 1 problem on the unit exam – standard hinge problem Honors Addition: no idea, but maybe next year we add the proofs for honors

CCSS 5.6 Inequalities in Two Triangles Objective:   Objective: Apply the Hinge Theorem or its converse to make comparisons in two triangles. Prove triangle relationships using the Hinge Theorem or its converse. Vocabulary: none CCSS

Converse of the Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is larger than the third side of the second triangle. Converse of the Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second triangle, then the included angle of the first is larger than the included angle of the second.

In DABC and DDEF, AC = DF, BC = EF, AB = 11”, ED = 15”, and mÐF = 58° In DABC and DDEF, AC = DF, BC = EF, AB = 11”, ED = 15”, and mÐF = 58°. Which of the following is a possible measure for ÐC, 45°, 58°, 80°, or 90°? Is there a hinge? In DGHI and DJKL, GH = JK, HI = KL, GI = 9’, mÐH = 45°, and mÐK = 65°. Which of the following is a possible for JL: 5’, 7’, 9’, or 11 feet?

In DRST and DXYZ, RT = XZ, ST = YZ, RS = 24 cm, XY = 18 cm, and mÐZ = 62°. What is possible measurement for ÐT? In DABC and DDEF, AB = DE, BC = EF, AC = 14”, mÐB = 70°, and mÐE = 40°. What is a possible length for DF?

In DABC and DCDB, AB = DC, AD = 12m, mÐABD = 56°, and mÐBDC = 48° In DABC and DCDB, AB = DC, AD = 12m, mÐABD = 56°, and mÐBDC = 48°. What do you know about sides AD and BC? B A Is there a hinge? C D

In DXYZ and DABC, mÐX = 56°, and mÐA = 68° In DXYZ and DABC, mÐX = 56°, and mÐA = 68°. What is true about their opposite sides? A C B X Y Z

In DWXZ and DXYZ, WZ = YZ, WX = 18m and XY = 11m In DWXZ and DXYZ, WZ = YZ, WX = 18m and XY = 11m. If mÐWZX = 56°, what can be said about ÐXZY? Y X Z W

Example 1 Compare the measures AD and BD. Answer: By the Hinge Theorem, mACD > mBCD, so AD > DB. Example 1

Example 1 Compare the measures mABD and mBDC. Answer: By the Converse of the Hinge Theorem, mABD > mBDC. Example 1

Example 1 Compare the lengths FG and GH. A. FG > GH B. FG < GH C. FG = GH D. not enough information Example 1

Example 1 Compare mJKM and mKML. A. mJKM > mKML B. mJKM < mKML C. mJKM = mKML D. not enough information Example 1

HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Nitan can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which leg can Nitan raise higher above the table? Answer: Nitan can raise his left leg higher above the table. If your doctor needed the hinge theorem to figure this out, find another doctor. Example 2

5-6 Example 2 Inequalities in Two Triangles LESSON Meena and Rita are both flying kites in a field near their houses. Both are using strings that are 10 meters long. Meena’s kite string is at an angle of 75° with the ground. Rita’s kite string is at an angle of 65° with the ground. If they are both standing at the same elevation, which kite is higher in the air? A. Meena’s kite B. Rita’s kite Example 2

Find the range of possible values for a. Example 3

Example 3 Find the range of possible values of n. Answer: 6 < n < 25 Example 3

Assignment Exit Slip: In ∆DEF DE = 3x, Due tomorrow: EF = x + 5 and DF = 15 and the perimeter is 64. What is the largest angle? Due tomorrow: 5.6 p376 #11-21 odd, 31-36, 38, 42 Chapter 5 Test Tuesday