9/14/15 CC Geometry UNIT: 1.1 - 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)

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.

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

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

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

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