1. 5-1 Bisectors of Triangles
You used segment and angle bisectors.
Identify and use perpendicular bisectors in triangles.
Identify and use angle bisectors in triangles.

2. Perpendicular Bisector
Perpendicular bisector is any segment that intersects another segment at its midpoint AND is perpendicular to that segment. K R S J

3. Perpendicular Bisector
A perpendicular bisector of a side of a triangle is a line perpendicular to a side through the midpoint of the side.
(Perpendicular and bisects one side only)
Perpendicular bisector B C A

4. Page 324

5. A. Find BC.
BC = AC Perpendicular Bisector Theorem
BC = 8.5 Substitution
Answer: 8.5

6. B. Find XY.
Answer: 6

7. C. Find PQ.
PQ = RQ Perpendicular Bisector Theorem
3x + 1 = 5x – 3 Substitution
1 = 2x – 3 Subtract 3x from each side.
4 = 2x Add 3 to each side.
2 = x Divide each side by 2.
So, PQ = 3(2) + 1 = 7.
Answer: 7

8. A. Find NO.
A. 4.6
B. 9.2
C. 18.4
D. 36.8

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

10. Definitions
Concurrent lines – three or more lines intersect at a common point.
Point of concurrency – the point where concurrent lines intersect.
The point of concurrency is also called the circumcenter of the triangle

11. Concurrent Lines
If three or more coplanar lines intersect at the same point, they are concurrent lines.
The point of intersection is the point of concurrency.
Concurrent lines
Point of concurrency

12. Page 325

13. Page326

14. Angle Bisector
When an angle bisector is used in a triangle, it is a segment. The angle bisector cuts the angle in half and goes to the other side. A B C D
Angle bisector

15. Page 327

16. A. Find DB.
DB = DC Angle Bisector Theorem
DB = 5 Substitution
Answer: DB = 5

17. C. Find QS.
QS = SR Angle Bisector Theorem
4x – 1 = 3x + 2 Substitution
x – 1 = 2 Subtract 3x from each side.
x = 3 Add 1 to each side.
Answer: So, QS = 4(3) – 1 or 11.

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

19. B. Find the measure of HFI.
C. 15
D. 30

20. C. Find the measure of UV.
A. 7
B. 14
C. 19
D. 25
**Set equal to each other

21. Page 328

22. A. Find the measure of GF if D is the incenter of ΔACF.
B. 144
C. 8
D. 65
**Use Pythagorean Theorem

23. B. Find the measure of BCD if D is the incenter of ΔACF.

24. 5-1 Assignment
Page 329, 2-30 even, skip 4