English

In How Many Points a Line, Not in a Plane, Can Intersect the Plane?

Advertisements
Advertisements

Question

In how many points a line, not in a plane, can intersect the plane?

Answer in Brief
Advertisements

Solution

A line which is not present in the plane can intersect the plane at only one single point. 

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Introduction to Euclid’s Geometry - Exercise 9.2 [Page 9]

APPEARS IN

R.D. Sharma Mathematics [English] Class 9
Chapter 9 Introduction to Euclid’s Geometry
Exercise 9.2 | Q 5 | Page 9

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Consider two ‘postulates’ given below:-

  1. Given any two distinct points A and B, there exists a third point C which is in between A and B.
  2. 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 two distinct lines can intersect?


In how many lines two distinct planes can intersect?


Euclid belongs to the country ______.


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:

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 ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.


Read the following two statements which are taken as axioms:

  1. If two lines intersect each other, then the vertically opposite angles are not equal.
  2. 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.


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.


The following statement is true or false? Give reason for your answer.

In the following figure, if AB = PQ and PQ = XY, then AB = XY.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×