TOPIC 1-7: MIDPOINTS, SEGMENT BISECTORS, & RAYS



TOPIC 2-5: SEGMENTS, MIDPOINTS, AND BISECTORS

|TERM |DEFINITION |SKETCH |

| | | |

|Midpoint |A point on a segment equidistant from both endpoints. | |

EXAMPLE 1 B is the midpoint of AC. AB = z + 2 and BC = 2z – 6.

Find “z”.

|TERM |DEFINITION |SKETCH |

| | | |

|Segment Bisector |A point, line, or plane that intersects a segment at its midpoint | |

EXAMPLE 2 B is between A and C. AB = 2y + 6, BC = y + 8, and

AC = 20. Find the value of “y” and determine if B is a

bisector.

Use the figure below to answer EXAMPLES 3 – 5.

EXAMPLE 3 If UY = 5, then find YV and UV.

EXAMPLE 4 If UY = 4x – 3 and YV = x, find UY and UV.

EXAMPLE 5 If UV = 18 and UY = 9, find YV.

Use the figure below to answer EXAMPLES 6 – 7.

EXAMPLE 6 If UV = x + 6 and UY = x – 1, find YV.

EXAMPLE 7 If UY = 3x - 6 and YV = x + 2, find UV.

NAME__________________DATE___________________PER.___

SEGMENTS, MIDPOINTS, & BISECTORS

W, R, and S are points on a number line, and W is the midpoint of RS. For each pair of coordinates given, find the coordinate of the third point.

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|R = 4, S = -6 |W = -4, S = 2 |

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|W = _______________ |R = _______________ |

Y is the midpoint of XZ. For each pair of points given, find the coordinates of the third point.

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|X( 5, 5 ), Z( -1, 5 ) |Z( 2, 8 ), Y( -2, 2 ) |

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|Y(________, ________) |X(________, ________) |

Find the indicated values.

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|B is between A and C. AB = 2x + 1, BC = 3x – 4, and AC = 62. Find the value of ‘x’, and determine if B is a bisector. |

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|x = _______________ |

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|Bisector: YES or NO? |

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|M is between L and N. LM = 7x – 1, MN = 2x + 4, and LN = 12. Find the value of ‘x’ an determine if M is a bisector. |

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|x = _______________ |

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|Bisector: YES or NO? |

Use the figure below for problem 7 below and 8 – 10 on the back. EC bisects AD at C. Find the value of “x” and the measure of the indicated segment.

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|AC = 3x + 6 and CD = 2x + 14 | |

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|x = _______________ | |

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|AC =_______________ | |

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|AC = 5x – 8 and CD = 16 – 3x | |

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|x = _______________ | |

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|AD = _______________ | |

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|AD = 6x – 4 and AC = 4x – 3 |10. AC = 3x – 1 and AD = 12 – x |

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|x = _______________ |x = _______________ |

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|CD = _______________ |CD = _______________ |

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U

Y

V

W

WY bisects UV at Y.

U

Y

V

W

WY bisects UV at Y.

A#2-5

A#2-5 PG. 2

A

C

D

E

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