Advertisements
Advertisements
Question
The following statement is true or false? Give reason for your answer.
There are an infinite number of lines which pass through two distinct points.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
Because only one line passes through two distinct points, in the following figure, it can be seen that only one line passes through points P and Q.
APPEARS IN
RELATED QUESTIONS
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.
In how many points a line, not in a plane, can intersect the plane?
In how many lines two distinct planes can intersect?
Given three distinct points in a plane, how many lines can be drawn by joining them?
The number of dimension, a point has ______.
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is ______.
The boundaries of the solids are curves.
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.
Read the following two statements which are taken as axioms:
- If two lines intersect each other, then the vertically opposite angles are not equal.
- If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.
Is this system of axioms consistent? Justify your answer.
