# 2.1 Segment Bisectors - PowerPoint PPT Presentation

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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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2.1 Segment Bisectors

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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

C

A

M

B

D

### 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 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

• 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 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 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

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

• Pg. 56 # 1-10