1. Segments and Angle Bisectors
Chapter 1 Section 1.5
Segments and Angle Bisectors

2. Warm-Up Name an acute angle. EBF or FBD 2. Name an obtuse angle.
ABF
3. Use the angle addition postulate to represent:
a. mABF mABE + mEBF = mABF
b. mEBD mEBF + mFBD = mEBD A B D

3. Midpoint
The midpoint of a segment is the point that divides the segment into two congruent segments
Bisect:
Two cut a figure in half A B C
Midpoint
Since B is the midpoint of , then

4. Segment Bisector
A segment, ray, line or plane that intersects a segment at its midpoint
Midpoint
Segment Bisector
• C P Q R
• D
Since is the Segment Bisector of , then

5. Use a ruler to measure the segment, and redraw the line segment
Use a ruler to measure the segment, and redraw the line segment. Then construct a segment bisector.

6. Midpoint formula
Used to find the midpoint of a segment with known endpoints
If A(x1, y1) and B(x2, y2) are the endpoints of segment AB, then the midpoint of segment AB has coordinates

7. Find the coordinates of the midpoint of a segment with the given endpoints
A(-3, 5) and B(5, -1)
Use the formula
C(-4, -3) and D(6, 3)
Use the formula

8. Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M
Use the formula
Remember the other endpoint is (x2, y2)
1. Find x2
2. Find y2
The other endpoint is (2, -1)

9. Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M
Use the formula
Remember the other endpoint is (x2, y2)
1. Find x2
2. Find y2
The other endpoint
is (2, -13)

10. Angle Bisector
A ray that divides an angle into two congruent adjacent angles • A B C • P
If is the angle bisector of BAC, then BAP  PAC

11. Use a protractor to measure and redraw the angle
Use a protractor to measure and redraw the angle. Then use a compass to find the angle bisector.

12. is the angle bisector of RPS
is the angle bisector of RPS. Find the two angle measures not given in the diagram. P
R •
T • •S 1
37° P
• R
T •
S • 2
44°
mRPT = mTPS = 37 °
mRPS = mRPT + mTPS
mRPS = 37° + 37 °
mRPS = 74°
mRPT = mTPS = 44 °
mRPS = mRPT + mTPS
mRPS = 44° + 44 °
mRPS = 88 °

13. is the angle bisector of ABC. Find the value of x.3.
(5x – 7)°
(3x + 13)°
Since ABC is bisected thus ABT  TBC
Which means:
mABT = mTBC
3x + 13 = 5x – 7
-2x + 13 = -7
-2x = -20
x = 10