Theorems on Solid Geometry

Some specific theorems on solid geometry are discussed here under this section.


The following two fundamental propositions may be considered as axioms:

Proposition 1: One and only one plane can be drawn through any two intersecting straight lines.

Proposition 2: Two intersecting planes cut one another in a straight line and in no other point outside the line of intersection.

The above two propositions lead to the following conclusions.

(a) A straight line intersects a plane at one point only or lies wholly in the plane or is parallel to the plane.

(b) Infinite number of planes can be drawn through a given straight line. 

(c) The straight line joining two given points on a plane lies wholly in the plane if it be produced indefinitely in either direction. 

(d) The position of a plane is determined if it passes through 

(i) two intersecting straight lines; 

(ii) a given straight line and a given point outside the line; 

(iii) two parallel straight lines; 

(iv) three non-collinear points.

Example: Show that two parallel lines and any of its transversal lie in the same plane. 

theorems on solid geometry

Let LM and NO be two parallel lines and XY, a transversal intersects LM at R and NO at S. We are to prove that the lines LM, NO and XY lie in the same plane (i.e., they are co-planar).

Proof: Since two parallel straight lines are co-planar, let us assume that the parallel tines LM and NO lie in the plane g. Now, the point R lies on the line LM and the point S on the line NO. Hence, it is evident that both the points R and S lie in the plane g. Therefore, the straight line joining the points R and S (i.e. the straight line XY) lies in the plane g.

Therefore, the straight lines LM, NO and XY lie in the same plane g.

Therefore, the straight lines LM, NO and XY are co-planar


11 and 12 Grade Math 

From Theorems on Solid Geometry to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More