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 Use the Perpendicular Bisector Theorems A. Find BC. Answer: 8.5

Example 1 Use the Perpendicular Bisector Theorems B. Find XY. Answer: 6

Example 1 Use the Perpendicular Bisector Theorems C. Find PQ. Answer: 7

Try with a partner A.4.6 B.9.2 C.18.4 D.36.8 A. Find NO.

TOO A.2 B.4 C.8 D.16 B. Find TU.

TOO A.8 B.12 C.16 D.20 C. Find EH.

Circumcenter Theorem

Example 2 (just watch.. Don’t write) Use the Circumcenter Theorem 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.

Example 2 (continued) Use the Circumcenter Theorem Answer: No, the circumcenter of an obtuse triangle is in the exterior of the triangle. 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

Think-Pair-Share 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. BILLIARDS A triangle used to rack pool balls is shown. Would the circumcenter be found inside the triangle?

Angle Bisectors

Example 3 Use the Angle Bisector Theorems A. Find DB. Answer: DB = 5

Example 3 Use the Angle Bisector Theorems B. Find m WYZ. Answer: m<WYZ = 28

Example 3 Use the Angle Bisector Theorems C. Find QS. Answer: So, QS = 4(3) – 1 or 11.

Verbally Answer A.22 B.5.5 C.11 D.2.25 A. Find the measure of SR.

Example 3 A.28 B.30 C.15 D.30 B. Find the measure of <HFI.

Example 3 A.7 B.14 C.19 D.25 C. Find the measure of UV.

Incenter Theorem

Example 4 Use the Incenter Theorem 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. a 2 + b 2 = c 2 Pythagorean Theorem SU 2 = 10 2 Substitution 64 + SU 2 = = 64, 10 2 = 100

Example 4 Use the Incenter Theorem Answer: ST = 6 Since length cannot be negative, use only the positive square root, 6. Since ST = SU, ST = 6. SU 2 = 36Subtract 64 from each side. SU= ±6Take the square root of each side.

Example 4 Use the Incenter Theorem B. Find m<SPU if S is the incenter of ΔMNP. Answer: m<SPU = (62) or 31 __ 1 2

Try with a Partner A.12 B.144 C.8 D.65 A. Find the measure of GF if D is the incenter of ΔACF.

TOO A.58° B.116° C.52° D.26° B. Find the measure of <BCD if D is the incenter of ΔACF.

Homework