Hello friends,
Today we are going to learn about points, lines, line segments and rays together.
Before we start our lesson please prepare your papers and pencils.
(wait…)
First we are going to talk about point.
Please press on your paper strongly with your pencil.
Now turn your paper inside out and touch your paper.
What you feel is the symbolic meaning of a point.
Lets examine the appearances of a point.
- A point is a geometrical term that has no size or dimension and it specifies location.
- It always denotes by capital letters.
For example we can call the point we made together point A.
Considering that we understood the meaning of a point, we can talk about the meaning of a line.
First of all we need to know that a line is made of infinite number of points.
To understand the symbolic meaning of a line please grab a ruler.
(wait…)
Now hold the long side of the ruler and move your hand back and forward on one of the ruler’s edge.
Our line model is a smooth line made of infinite number of points.
To talk about the basic appearance of a line,
- Line is a smooth and endless geometrical term which has no thickness but lenght.
- to draw a line we need at least two points.
- Lines are either named by two points on it or named with lower case letters.
For example if we consider that A and B are points on your ruler and your ruler has an infinite length. We can call it the AB line. Or we can call it the line c, with lower case.
Lets give some examples of lines in our daily lives.
- If a ribbon could extend to infinite it would be a line example.
- If a rectangular desk’s edge could extend to infinite it would be a line example.
Now you find an example.
(wait…)
That’s really a creative idea! Share your answer with your teacher and be sure that it is correct.
Lets remember what we learned until now.
Point and line…
Points have no dimension and
Lines are made of infinite number of points.
Lets put together the two terms that we learned today.
- We call two points which lay on the same line collinear.
- Two dots are always collinear, that means they are always on the same line.
So, are 3 points points always collinear?
(wait…)
No, three or more points may not always be on the same line.
Now lets intensify the things that we learned about points and lines.
First you will listen to the questions, please try to answer before the time finishes and the correct answer will be explained.
Please listen carefully, check your answers and repeat the topic.
Question 1-How many lines can pass through 2 points?
A)0 B)1 C)2 D)infinite
(wait…)
The answer is B. Only ONE line passes through two points.
And we call those points collinear.
Question 2-How many lines can pass through a point?
A)1 B)2 C)3 4)infinite
(wait…)
The answer is D. Infinite number of lines can pass through a point.
Question 3-How many points are there in a line?
(wait…)
A line is made of infinite number of points.
We finished our questions. Now we can move on to another topic.
Line Segment
As we can understand from the term itself a line segment is a part of the infinitely extending line. This means that a line segment has a starting point and an ending point unlike a line. Line segment contains every point on the line between its endpoints.
Now please grab your rulers again.
(wait…)
Like we did in the beginning hold one of the rulers edges and start to move your hand.
But this time instead of thinking it will extend infinitely in both directions stop at the end of the ruler. And think the ends of the ruler as the distinct end points of the line segment.
The line segments have two linked points and can’t go beyond them. That’s why we are able to measure the length of line segments. Line segment is only a part of a line.
Now,lets talk about the appearance of a line segment:
- It is a piece of a line bounded by two distinct end points.
- We can measure its length.
- We name them by the capital letters of the ending points written in brackets.
This time you can name our symbolic ruler example.
(wait…)
Let’s check,
Lets call our rulers starting point as E and the ending as C.
We will write our line segments name as
(slowly)
Capital E and Capital C in brackets.
Now we can move on to our last topic Ray.
Ray
Let’ again grab our rulers.
(wait…)
This time lets recognize our starting point carefully . Then lets move our hand on the edge and think that this edge extends infinitely in that direction.
This is our way of defining ray.
So ray has an initial point and it goes to infinity in other direction.
In other words;
A ray, has one fixed endpoint, and extends infinitely along the line from the endpoint. It has no thickness.
Rays are written similar to line segments but unlike line segments, you leave one side open.
For example if our starting point is M and any point on the infinite direction is N, our ray will be written as:
Open bracket capital M, capital N.
Homework:
Please give 3 examples from your daily life for line,line segment and ray. You can check these examples with your teacher.
Our lesson has finished.
I am really glad that we had this learning experience together and thank you for your participation.
