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प्रश्न
How many lines can be drawn through a given point.
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उत्तर
Given a single point, then we can draw infinite number of lines through that point.
For example: If we have a point A, then there are infinite numbers of lines passing through it.
Here, lines m, n, o and p all pass through point A.
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संबंधित प्रश्न
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?
The number of dimensions, a surface has ______.
Which of the following needs a proof?
The statements that are proved are called axioms.
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
Solve the following question using appropriate Euclid’s axiom:
Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, if OX = `1/2` XY, PX = `1/2` XZ and OX = PX, show that XY = XZ.
In the following figure AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.
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.
