Euclid

Euclid has given many postulates. Here, we will discuss 5 of Euclid's postulates of them.

1st Euclid's postulates state that two points determine a line segment. In other words, we can say a straight line may be drawn from anyone point to any other point.

In this example, we see that only one line is drawn from these two points P and Q.

2nd Euclid's postulates states that a line segment can be extended indefinitely along a line.

We have a line segment AB, we have two endpoints A and B on this line, and the line segment can be produced from both sides to form a straight line.

And in 3rd Euclid's postulates, he states that a circle can be drawn with a center and any radius. This is the center of a circle and this is the radius of a circle.

The 4th Euclid's postulates states that all right angles are congruent. In other words, we can say that all right angles are equal to one another.

For example, we have two right angles P and Q. Angle P is equal to angle Q since both are right angles.

Let us arrange the angles in such a way that the orientation of the angle has changed. You can observe that after changing the orientation, angle P remains equal to angle Q.

The 5th Euclid's postulates states: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Here angle 1= 70° and angle 2 = 100°. Adding 1 & 2 we have 170° which is less than 180°.

Now let us produce the lines of the side at which these angles lie. On production, we can see that the 2 lines intersect as stated in the postulate.

Read More: Euclid Geometry Class 9: Introduction To Euclid's Geometry - Maths