1.5 Segment and Angle Bisector

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1.5 Segment and Angle Bisector

• Bisect a segment and an angle

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Definition of the Midpoint

• A midpoint bisects a segment into two equal
  segments.
• A M B
• So AM MB

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A Line can also bisect

• Here Line XY bisects CD at Q
• Y
• C Q D
• X
• Thus CQ QD

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WE can find a segment bisector by folding paper

• Draw a line and mark the end point dark.
• Fold the paper to put one endpoint over the other
  endpoint.
• Where the paper is folded is the midpoint of the
  segment.

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Midpoint FormulaHow to find the midpoint on a
graph

• Given the endpoints (x,,y1) and (x2, y2) of the
  Line segment we can use the formula
• Let the endpoint be (2, 8) and (6, 2)

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What if you are just given the Midpoint and an
endpoint

• Midpoint (5, 6) and endpoint (6,4)
• 6 x 10 4 y 12
• x 4 and y 8 other endpoint (4,8)

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Angle bisector

• If YM is the angle bisector,
• then
• X M
• Y
• Z

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Some work with Angle bisectors

• X MP bisect
• P
• M B

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Solve for x

• BX bisect
• A
• X Solve for X
• B
• C

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Solve for x

• BX bisect
• A
• X Solve for X
• B
• C 2x 6 3x 2
• 4 x

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Homework

• Page 38 40
• 17- 29 odd
• 31 33
• 38 42
• 44 49, 52, 54