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MODELING MONDAY RECAP Take the last power of 2 that occurs before the number of seats. Take the number of seats minus that power of 2. Take that answer and multiply by 2 and then add 1. This is your seat you should pick! Chapter 5: Relationships in Triangles • New Homework Calendar • Chapter 5 test: December 19th 5-1 BISECTORS OF TRIANGLES Objective: Identify and use perpendicular bisectors and angle bisectors in triangles. Perpendicular Bisectors Example 1 A. Find BC. Answer: 8.5 Use the Perpendicular Bisector Theorems Example 1 B. Find XY. Answer: 6 Use the Perpendicular Bisector Theorems Example 1 C. Find PQ. Answer: 7 Use the Perpendicular Bisector Theorems Try with a partner A. Find NO. A. 4.6 B. 9.2 C. 18.4 D. 36.8 TOO B. Find TU. A. 2 B. 4 C. 8 D. 16 TOO C. Find EH. A. 8 B. 12 C. 16 D. 20 Circumcenter Theorem Example 2 (just watch.. Don’t write) GARDEN A triangular-shaped garden is shown. Can a fountain be placed at the circumcenter and still be inside the garden? By the Circumcenter Theorem, a point equidistant from three points is found by using the perpendicular bisectors of the triangle formed by those points. Use the Circumcenter Theorem Example 2 (continued) Copy ΔXYZ, and use a ruler and protractor to draw the perpendicular bisectors. The location for the fountain is C, the circumcenter of ΔXYZ, which lies in the exterior of the triangle. C Answer: No, the circumcenter of an obtuse triangle is in the exterior of the triangle. Use the Circumcenter Theorem Think-Pair-Share BILLIARDS A triangle used to rack pool balls is shown. Would the circumcenter be found inside the triangle? A. No, the circumcenter of an acute triangle is found in the exterior of the triangle. B. Yes, circumcenter of an acute triangle is found in the interior of the triangle. Angle Bisectors Example 3 A. Find DB. Answer: DB = 5 Use the Angle Bisector Theorems Example 3 B. Find m Ð WYZ. Answer: m<WYZ = 28 Use the Angle Bisector Theorems Example 3 C. Find QS. Answer: So, QS = 4(3) – 1 or 11. Use the Angle Bisector Theorems Verbally Answer A. Find the measure of SR. A. 22 B. 5.5 C. 11 D. 2.25 Example 3 B. Find the measure of <HFI. A. 28 B. 30 C. 15 D. 30 Example 3 C. Find the measure of UV. A. 7 B. 14 C. 19 D. 25 Incenter Theorem Example 4 A. Find ST if S is the incenter of ΔMNP. By the Incenter Theorem, since S is equidistant from the sides of ΔMNP, ST = SU. Find ST by using the Pythagorean Theorem. a2 + b2 = c2 Pythagorean Theorem 82 + SU2 = 102 Substitution 64 + SU2 = 100 82 = 64, 102 = 100 Use the Incenter Theorem Example 4 SU2 = 36 SU = ±6 Subtract 64 from each side. Take the square root of each side. Since length cannot be negative, use only the positive square root, 6. Since ST = SU, ST = 6. Answer: ST = 6 Use the Incenter Theorem Example 4 B. Find m<SPU if S is the incenter of ΔMNP. 1 (62) or 31 Answer: m<SPU = __ 2 Use the Incenter Theorem Try with a Partner A. Find the measure of GF if D is the incenter of ΔACF. A. 12 B. 144 C. 8 D. 65 TOO B. Find the measure of <BCD if D is the incenter of ΔACF. A. 58° B. 116° C. 52° D. 26° Homework