1. 9/14/15
CC Geometry
UNIT: Tools of Geometry
LESSON: 1.1c – Midpoints of segments
MAIN IDEA: Students will be able to use information to determine midpoints and lengths of segments.
HOMEWORK: Worksheet 1.1c (Both)
DO NOW: Find the distance between the following points in simplest radical form.
1) (2,1) and (8,7) 3) (-2,0) and (3,10)

2. Midpoint
The midpoint of a segment divides a segment into two congruent segments.
NOTE** Two segments are congruent if they are equal in length
Example: We would say M is the midpoint of segment AB if and only if…
𝐴𝑀≅𝑀𝐵
NOTE** Congruence is noted using the symbol ≅.
Congruence is also represented by a dash through congruent segments.

3. Let’s take a look at a few examples!!
Determine the midpoint of segment HI.
Determine the midpoint of segment GH.
Determine the midpoint of segment FI.
Think About It….
Can we derive a general rule for finding the midpoint between any two points on the number line using their coordinates?
Midpoint of segment AB= 𝐴+𝐵 2

4. Midpoint in the Coordinate Plane
Use the diagram below to find the midpoint of the segment AB:
What is the midpoint of the x-coordinates? y-coordinates?
𝑥=−1, 𝑦=2
Midpoint =(−1, 2)
The midpoint of a segment with endpoints 𝑥 1 , 𝑦 1 𝑎𝑛𝑑 𝑥 2 , 𝑦 2 can be measured using the formula…
Think on it…
Can we think of a general formula? B A

5. Bisector
A segment bisector is any geometric figure that intersects a segment at its midpoint.
A segment bisector divides a segment into two congruent segments.
NOTE** A segment bisector can be a point, line, segment, ray or plane!
Examples
AB bisects PQ Point M bisects AB

6. Let’s look at an example…
M is the midpoint of PQ. PM = 6x + 7 and MQ = 9x – 8, find the length of PQ.