1. Chapter 5: Relationships in Triangles
New Homework Calendar
Chapter 5 test: December 19th

2. 5-1 bisectors of Triangles

3. Perpendicular Bisectors

4. Example
Find BC.
Answer: 8.5

5. Example
Find XY.
Answer: 6

6. Example
Find PQ.
Who wants to explain it?
Answer: 7

7. TOO
Find NO.
A. 4.6
B. 9.2
C. 18.4
D. 36.8

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

9. TWAP
Find EH.
A. 8
B. 12
C. 16
D. 20

10. Circumcenter Theorem

11. Example (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.

12. Example (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.

13. 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.

14. Angle Bisectors

15. Example
A. Find DB.
Answer: DB = 5

16. Example
Find m WYZ.
Answer: m<WYZ = 28

17. Example
Find QS.
Answer: So, QS = 4(3) – 1 = 11.

18. TOO
Find the measure of SR.
A. 22
B. 5.5
C. 11
D. 2.25

19. Incenter Theorem

20. Example Find ST if S is the incenter of ΔMNP.
Find ST by using the Pythagorean Theorem.
a2 + b2 = c2 Pythagorean Theorem
82 + SU2 = 102
64 + SU2 = 100

21. Example 4 SU2 = 36 SU = 6 Take the square root of each side.
Since ST = SU, ST = 6.
Answer: ST = 6

22. TWAP (Hint: Use Pyth. Thm)
A. Find the measure of GF if D is the incenter of ΔACF.
A. 12
B. 144
C. 8
D. 65
Find <C
<F=58
<A=70
<C=52

23. Homework
Pg. 329 #9 - 14, 17-30, 32-35, 48, 54