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प्रश्न
How many planes can be made to pass through two points?
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उत्तर
Given two distinct points, we can draw many planes passing through them. Therefore, infinite number of planes can be drawn passing through two distinct points or two points can be common to infinite number of planes.
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संबंधित प्रश्न
The following statement is true or false? Give reason for your answer.
Only one line can pass through a single point.
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.
How many planes can be made to pass through three distinct points?
The number of dimensions, a surface has ______.
The number of dimension, a point has ______.
Euclid divided his famous treatise “The Elements” into ______.
A pyramid is a solid figure, the base of which is ______.
Read the following statement :
An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each.
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.
Read the following statements which are taken as axioms:
- If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
- If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
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.
