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1.5 Notes Segment and Angle Bisectors

1.5 Notes Segment and Angle Bisectors. Midpoint. 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. Segment Bisector. Midpoint Formula. When given two points A (x 1 , y 1 ) and B (x 2 , y 2 ):.

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1.5 Notes Segment and Angle Bisectors

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  1. 1.5 Notes Segment and Angle Bisectors

  2. Midpoint • 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 Segment Bisector

  3. Midpoint Formula When given two points A (x1, y1) and B (x2, y2):

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

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

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

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

  8. Angle Bisector • A ray that divides (or bisects) an angle into two adjacent angles that are congruent • BD is an angle bisector so:

  9. 42/2 = 21o 42o Ex 5) JK bisects angle HJL. Given that HJL = 42o, what are the measures of the angles HJK and KJL?

  10. 47(2) = 94o 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.

  11. (x + 10)o (3x – 20)o 3x – 20 = x + 10 2x – 20 = 10 2x = 30 x = 15 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.

  12. ABD = 2(15) + 50 2x + 50 = 5x + 5 = 80o 50 = 3x + 5 =CBD 45 = 3x ABC = 80(2) x = 15 ABC = 160o 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.

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