1-5+Bisectors

1-5 Bisectors Matthew Saidel James Morriarty

__Summary__ This section will teach how to bisect a segment and angle using bisectors. To do this you will need to know what a bisector and midpoint is. Also you will need to know the midpoint formula. Next you will need to know what an angle bisector is and how to find out where it is. This section will teach you a few new equations and ways to find the bisector of a segment or angle.

__Web Pages that teach you how to find bisectors of angles and segments.__ [] []

__Vocabulary__ Midpoint- The point that divides. Bisects- the segment is put into two congruent segments. Segment Bisector- is a segment, ray, line, or plane that intersects a segment at its midpoint.

__Formulas__ Midpoint Formula __Sample Problems with solutions__ Example 1 Find the coordinates of the midpoint of with endpoints //A//(–2, 3) and //B//(5, –2).
 * This Came from the book**




 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]]
 * Use the Midpoint Formula as follows.[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||

Example 2 The midpoint of is //M//(2, 4). One endpoint is //R//(–1, 7). Find the coordinates of the other endpoint.
 * This came from the book**


 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]]
 * Let (//x, y//) be the coordinates of //P//. Use the Midpoint Formula to write equations involving //x// and //y//.[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||


 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/mcd_ma_geo_lsn_0395937779_p34_f11.gif align="top"]][[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||

The ray bisects the angle //EFG//. Given that //m////EFG// = 120°, what are the measures of //EFH// and //HFG//?
 * This came from book**
 * Example 3**



//m////EFH// = //m////HFG// = = 60°.
 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]]
 * An angle bisector divides an angle into two congruent angles, each of which has half the measure of the original angle. So,[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||

__Practice Problems__ //C//(3, 0), //M//(3, 4) //A//(–1, –9), //B//(11, –5)**,** //A//(5, 4), //B//(–3, 2) //A//(0, 0), //B//(–8, 6)
 * Find the coordinates of the other endpoint of a segment with the given endpoint and midpoint //M//.**
 * Find the coordinates of the midpoint of a segment with the given endpoints.**
 * Find the coordinates of the midpoint of a segment with the given endpoints.**