Segments and rays room under the subset the lines. A segment is a part of a line having two endpoints and also has a details length. ~ above the other hand, a ray is likewise a part of line having actually one endpoint and also the various other direction extend indefinitely. Figure 1 illustrates a segment and also a ray.


A segment is a collection of points consisting of 2 points of the line dubbed the endpoints, and every one of the clues of the line between the endpoints. That is commonly used to represent the length, height, or broad of a certain object and the distance between two objects. That is named by making use of the brand of that is endpoints and insert a line (( ) ̅) over the letters. Figure 2 mirrors segment ab which can likewise be created as (AB) ̅.

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Draw 2 points and label it together C and also D.

Connect the two points right each other.

prize : 6


Use the point out in the line together endpoints the the segments.

The segments are (QR) , (RS) , (ST) , (QS) , (RT) , and (QT) .

A midpoint the a segment is the point that divides the line segment right into two congruent parts. The is situated at the facility of the segment. Number 3 reflects the midpoint that a segment.


Note: The 2 vertical lines show that the distances from the midpoint come both endpoints are equal.

Answer: 6


The midpoint Z divides (XY) into two congruent parts: (XZ) and also (YZ) .

The length of (XZ) is ½ the length of (XY) which is ½ 12 = 6.

Answer: 18


The midpoint O divides (NP) ̅ right into two congruent parts: (NO) ̅ and (PO) ̅.

sThe size of (NP) ̅ is twice the size of (NO) ̅ i beg your pardon is 2 9 = 18.

Addition and Subtraction the Segments

Figure 4 illustrates three collinear points E, F, and also G developing a segment.


Points E and G constitute the endpoints the the segment i m sorry is (EG) and suggest F in between divides (EG) into two segments: (EF) and (FG) . The sum of the lengths of (EF) and (FG) is same to the length of (EG) . Therefore, (EF) + (FG) = (EG) . The expression to represent a segment if suggest F is in between Points E and G.

The adhering to expressions are additionally true because that the lengths that the segments:

(EF) = (EG) – (FG)

(FG) = (EG) – (EF)

example 5

Find the length of (JL) in the figure.


Answer: 10


Points J and L space endpoints of (JL) and point K is between points J and L.

Therefore, (JK) + (KL) = (JL) .

(JL) = 6 + 4 = 10.

example 6

The length of (UV) is 13 and W is in between points U and also V. If (WU) = 5, what is the length of (VW) ?

Answer: 8

Points U and V room endpoints that (UV) and point W is in between points U and V.

Therefore, (UW) + (VW) = (UV) .

(UW) = (WU) = 5

So, (VW) = (UV) - (UW) = 13 – 5 = 8.

Definition of a Ray

A ray is composed of a allude on a line and all points on one side of the point. It has actually only one endpoint. Light ray are typically used in physics to signify direction and also force. In naming a ray, consider two clues in the ray: one is the endpoint and the various other is any point in the ray. The label of the endpoint should be the very first letter that the surname of the ray and also place a right arrow sign ( ( ) ) over the letters. Number 5 illustrates a beam labeled together (RY) .


Opposite rays space two rays that lie top top the exact same line having a common endpoint and also no other suggest in common. In number 6 shown, (RS) ̅ and also (ST) ̅ room opposite rays.

example 7

Draw (AE) .



Draw 2 points and also labeled it as A and E.

Connect the 2 points directly each other and extend the line from suggest E.

example 8

Find the variety of rays that have the right to be found in the line.


Explanation: 12

Consider two points in the line as the point out of the ray.

Rays pointing come the right deserve to be named as (MB) , (BP) , (PC) , (MP) , (BC) , and (MC) .

Rays pointing to the left have the right to be named as (CP) ,(PB) , (BM) , (CB) , (PM) , and (CM) .

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There are 12 rays that are found in the line.

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