Measuring Segments

Objectives:

• Calculate the distance between two points

• Set up and solve linear equations using segment addition and midpoint properties

• Correctly use notation for distance and segments

• distance The absolute value of the difference of the coordinates. Also called the length.

Example:

The distance from R to S is written RS

Distance is alwaysalwaysalwaysalways positive. If you come up with a negative answer, you’ve done something wrong!

Notation: Notice the different notations:

AB line AB

segment AB

AB length AB

R S

AB

= − − = − =RS 2 3 5 5

congruent segments

Segments that have the same length.

Notation: “Tick marks” indicate congruent segments.

YX

A B

Since XY AB, XY AB= ≅

• •

t

between Point B is between two points A and C if all three points are collinearcollinearcollinearcollinear and

AB + BC = AC.

(part + part = whole)

Note: This is also called the Segment Segment Segment Segment Addition PostulateAddition PostulateAddition PostulateAddition Postulate.

●

A B C

bisect

midpoint

To cut or divide into two congruent pieces.

Example:

Point B bisects bisects bisects bisects FI ⇒ FB = BI

The point that bisects a segment.

Example: Point B is the midpointmidpointmidpointmidpoint of

●

F B I

FI

Examples 1. O is the midpoint of and DO = 16. Find DG.

2. K is the midpoint of and SY = 24. Find SK.

3. E is the midpoint of ; SE = 2x + 7 and EA = 5x — 2. Find SA.

DG

SY

SA

●

D O G

16

●

S K Y

24

●

S E A

2x+7 5x—2

DO + OG = DG16 + 16 = 32

SK = ½ SY = ½(24) = 12

SE = EA2x + 7 = 5x — 2

9 = 3xx = 3

SA = SE + EA= 2(3)+7+5(3)-2= 26

construction A method of geometric drawing that uses only a compass and a straightedge.

Constructing a figure is different from just sketching it. Construction has been used in Geometry since ancient times, in both philosophical and practical ways.

In class, you will learn to construct

• congruent segments

• segment midpoints

• segment bisectors