1.5 Notes Segment and Angle Bisectors.  The point that divides (or bisects) a segment into two congruent segments.  A segment, ray, line, or plane that.

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Presentation transcript:

1.5 Notes Segment and Angle Bisectors

 The point that divides (or bisects) a segment into two congruent segments.  A segment, ray, line, or plane that intersects a segment at its midpoint

When given two points A (x 1, y 1 ) and B (x 2, y 2 ):

Ex 1) Find the midpoint of DE with endpoints D(3,5) and E(-4, 0)

Ex 2) Find the midpoint of PQ with endpoints P(0, -7) and Q(-2, -1)

Ex 3) The midpoint of XY is M(3, -4). One endpoint is Y(-3,-1). Find the coordinates of the other endpoint.

Ex 4) The midpoint of JK is M(0, ½ ). One endpoint is J(2, -2). Find the coordinates of the other endpoint.

 A ray that divides (or bisects) an angle into two adjacent angles that are congruent  BD is an angle bisector so:

Ex 5) JK bisects angle HJL. Given that HJL = 42 o, what are the measures of the angles HJK and KJL? 42 o 42/2= 21 o

Ex 6) A cellular phone tower bisects the angle formed by the two wires that support it. Find the measure of the angle formed by the two wires. 47(2)= 94 o

Ex 7) In the diagram, MO bisects angle LMN. The measures of the two congruent angles are (3x – 20) o and (x + 10) o. Solve for x. 3x – 20 = x x – 20 = 10 (3x – 20) o (x + 10) o 2x = 30 x = 15

Ex 8) In the diagram BD bisect angle ABC. Find x and use it to find the measures of the angles ABD, DBC, and ABC. 2x + 50 = 5x = 3x = 3x x = 15 ABD = 2(15) + 50 = 80 o =CBD ABC = 80(2) ABC = 160 o