Advertisements
Advertisements
Question
Consider two ‘postulates’ given below:-
- Given any two distinct points A and B, there exists a third point C which is in between A and B.
- There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.
Advertisements
Solution
Yes, these postulates include undefined terms like 'point and line'. Furthermore, these postulates are consistent because they deal with two distinct situations:
- States that given two points, A and B, a point C exists on the line that connects them. Whereas
- States that given points A and B, you can select a point C that is not on the line that connects them.
No, these postulates are not derived from Euclid's postulates but rather from the axiom, "Given two distinct points, there is a unique line that passes through them."
APPEARS IN
RELATED QUESTIONS
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
perpendicular lines
The number of dimensions, a solid has ______.
In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio ______.
Which of the following needs a proof?
“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
In the following figure BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
The following statement is true or false? Give reason for your answer.
A terminated line can be produced indefinitely on both the sides.
The following statement is true or false? Give reason for your answer.
If two circles are equal, then their radii are equal.
