1-5+Bisectors

Summary: In this lesson we will be learning about midpoints and bisectors. By the end of this lesson you will know how to calculate a midpoint and how to find a bisector. There are two ways to find the midpoint. When you have the two coordinates or when it is given and you have to find the endpoint. A bisector can be used in a segment or and angle, mainly we will be focusing on angles.

Find in textbook pages: 34-340

Vocabulary: Midpoint: of a segment is the point that divides equally Bisects: a point that divides the segment into two congruent segments Segment bisector: a segment, ray, line, or plane that intersects a segment at its midpoint Midpoint formula: an equation that allows you to find the mid point with two sets of coordinates. Formula: Midpoint: (x1+x2/2, y1+y2/2) Angle bisectors: a ray that divides an angle into two adjacent angles that are congruent

Example 1: Find the coordinates for the midpoint of segment AB, with the endpoints of A (-2,3) and B (5, -2).

Solution:

M= (-2+5/2, 3+ -2/2) M= (3/2, ½) Example 2: The midpoint of RP is M (2,4). One of the endpoints R (-1,7). Find the coordinates of the other endpoint.

Solution: Because (2,4) is the midpoint you make them into two separate equations. You would have the x coordinates equal 2 and the y coordinates equal 4.

(2,4)= (-1+x/2, 7+y/2)

2= -1+x/2 4=7+y/2 4= -1+x 8= 7+y 5= x 1=y

P (5,1)



Example 3: In the diagram ray RQ bisects angle PRS. The measure of the two congruent angles are (x+40) degrees and (3x-20). Solve for x.

X+ 40= 3x-20 40= 2x-20 60= 2x 30= x



Review Problems: 1) X (0,0) Y (-8,6)

2) X (10,8) Y (-2,5)

3) Angle ABD: 2x+35 and angle CBD: 5x-22

4) Angle ABD: 1/2x+20 and angle CBD: 3x-85

Helpful Websites to get more lessons: - for a segment bisector: http://www.icoachmath.com/SiteMap/SegmentBisector.html - segment bisector video http://www.watchknow.org/Video.aspx?VideoID=20214 - - midpoint example http://www.youtube.com/watch?v=bcp9pJxaAOk -