1. Essentials of geometry
Midpoints and Bisectors
Ch 1.4
C. N. Colón
Geometry
St Barnabas HS Bronx, NY

2. Midpoint The point that bisects a segment.
means split into 2 equal or congruent segments
A M B
If M is the midpoint of AB, then AM = MB
AM = ½ AB and MB = ½ AB
AB = 2AM and AB = 2MB ~

3. Midpoint
A M B
For any line segment AB, if the coordinate of A is a, and the coordinate of B is b, then the coordinate of the midpoint of AB is
a + b 2
-3 + 5 2
= = 1, the midpoint M

4. Always Remember!
If objects are congruent, then you can set their measures equal to each other!

5. Midpoint
12x x+5
A M B
12x+3=10x+5
2x=2
x=1

6. Bisector of a segment
A bisector of a line segment is any segment, ray, line, or plane that intersects a segment at its midpoint. A B M l

7. Add & Subtract line segments
REMEMBER: A B x1 x2
The length of AB can be found by x2-x1
The symbol for the length of AB is AB.

8. Add & Subtract line segmentsP Q R S
PQ = |(-1) – (-3)| = |-1 + 3| = 2
PR = |0 – (-3)| = |0 + 3| = 3
QR = |0 – (-1)| = |0 + 1| = 1
RS = | 3 – 0| = |3| = 3
QS = |3 – (-1)| = |3 + 1| = 4
PS = |3 – (-3)| = |3 + 3| = 6

9. Add & Subtract line segmentsP Q R S
PR = RS and
PR + RS = PS
R is the midpoint of PS
PQ + QS = = 6
and PS = 6 
PQ + QS = PS

10. Homework
Read pp , p. 13 # 1-12 (odd)