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1.5 Segment & Angle Bisectors

1.5 Segment & Angle Bisectors. Objectives:. Students will understand geometric concepts and applications. Objectives: Bisect a segment. Bisect an angle. Always Remember!. If they are congruent, then set their measures equal to each other!. Midpoint. The point that bisects a segment.

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1.5 Segment & Angle Bisectors

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  1. 1.5 Segment & Angle Bisectors

  2. Objectives: Students will understand geometric concepts and applications. Objectives: • Bisect a segment. • Bisect an angle.

  3. Always Remember! • If they are congruent, then set their measures equal to each other!

  4. Midpoint • The point that bisects a segment. • Bisects? splits into 2 equal pieces A M B 12x+3 10x+5 12x+3=10x+5 2x=2 x=1

  5. Segment Bisector • A segment, ray, line, or plane that intersects a segment at its midpoint. k A M B

  6. Compass & Straightedge • Tools used for creating geometric constructions

  7. Midpoint Formula • Used for finding the coordinates of the midpoint of a segment in a coordinate plane. • If the endpoints are (x1,y1) & (x2,y2), then

  8. Ex: Find the midpoint of SP if S(-3,-5) & P(5,11).

  9. Practice • Find the midpoint for the following: • A(8, 4), B(12, 2) • C(9, 5), D(17, 4) • E(-11, -4), F(-9, -2) • (10, 3) • (13, 4.5) • (-10, -3)

  10. Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.

  11. Angle Bisector • A ray that divides an angle into 2 congruent adjacent angles. BD is an angle bisector of <ABC. A D B C

  12. Ex: If FH bisects EFG & mEFG=120o, what is mEFH? E H F G

  13. Last example: Solve for x. * If they are congruent, set them equal to each other, then solve! x+40o x+40 = 3x-20 40 = 2x-20 60 = 2x 30 = x 3x-20o

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