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S ECTION 1.5 SEGMENT AND ANGLE BISECTORS

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A N ANGLE BISECTOR IS THE RAY THAT DIVIDES ( OR BISECTS ) AN ANGLE INTO CONGRUENT ADJACENT ANGLES. O M G N

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H OW CAN WE USE THIS INFORMATION ABOUT ANGLE BISECTORS ? (x+40)° (3x – 20)° P Q RS

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A MIDPOINT IS THE POINT THAT DIVIDES ( OR BISECTS ) THE LINE SEGMENT INTO EQUAL PARTS. T HE EQUAL PARTS ARE ALSO CALLED CONGRUENT SEGMENTS. D E3 m L To Bisect means to divide in ½ DL = LE To be congruent means to be equal

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D ON ’ T FORGET ABOUT ANGLE ADDITION AND SEGMENT ADDITION POSTULATES !

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C AN WE BISECT A LINE ? W HY OR WHY NOT ? Take a minute to write down your response.

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B ACK TO MIDPOINTS! You will sometimes see midpoints on a coordinate plane. The MIDPOINT FORMULA will allow you to find the x and y coordinates for the midpoint. P(1,2) Q(3,-2) How do we find that midpoint?

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MIDPOINT FORMULA The x for the midpoint = The y for the midpoint = Add the 2 and divide by 2 (sound familiar?)

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L ET ’ S PRACTICE THE M IDPOINT F ORMULA A (5, 4) and B(3, 2) A(-1, -9) and B(11, -5) A(6, -4) and B(1, 8) C(3, 0) and M(3,4) D(5,2) and M(7,6) E(-4,2) and M(-3,-2) FIND THE MIDPOINT (M) FIND THE ENPOINT

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Warm up (draw each one) 1) Vertical line m intersects a horizontal plane M at point O. 2) Horizontal plane P contains two lines k and n that intersect.

Warm up (draw each one) 1) Vertical line m intersects a horizontal plane M at point O. 2) Horizontal plane P contains two lines k and n that intersect.

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