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2.1 Segment Bisectors. Definitions. Midpoint – the point on the segment that divides it into two congruent segments. A. M. B. Definitions. Segment bisector – a segment, line, ray, or plane that intersects a segment at its midpoint Bisect – to divide the segment into two congruent segments.

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Presentation Transcript

Definitions
Definitions

  • Midpoint – the point on the segment that divides it into two congruent segments

A

M

B


Definitions1
Definitions

  • Segment bisector – a segment, line, ray, or plane that intersects a segment at its midpoint

  • Bisect – to divide the segment into two congruent segments

C

A

M

B

D


Find segment lengths
Find Segment Lengths

  • M is the midpoint of AB. Find AM and MB.

  • AM = MB = ½ (AB)

  • = ½ (26)

  • = 13

26

A

M

B


Find segment lengths1
Find Segment Lengths

  • P is the midpoint of RS. Find PS and RS.

  • RP = PS so PS = 7

  • RS = 2 (RP)

  • = 2 (7)

  • = 14

R

P

S

7


Use algebra with segment lengths
Use Algebra with Segment Lengths

  • Line l is a segment bisector of AB. Find x.

    AM = MB

    5x = 35

    x = 7

5x

35

A

M

B

l


The midpoint formula
The Midpoint Formula

  • The coordinates of the

    midpoint of a segment

    are the averages of the

    x-coordinates and the

    y-coordinates of the

    endpoints

B

y2

y1 + y2

----------

2

M

A

y1

x1

x1 + x2

---------

2

x2


The midpoint formula1
The Midpoint Formula

  • The coordinates of the

    midpoint of AB is:

    M x1 + x2 , y1 + y2

    2 2

B

y2

y1 + y2

----------

2

M

A

y1

x1

x1 + x2

---------

2

x2


Example
Example

B (7, 4)

M

A (1, 2)

1

1

Let (x1, y1) = (1, 2)

Let (x2, y2) = (7, 4)

M = 1 + 7 , 2 + 4

2 2

= (4, 3)


Guided practice
Guided Practice

  • Pg. 56 # 1-10