Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
We know that, if two lines intersect each other, then the vertically opposite angles are equal. It is a theorem, So given Statement I is false and not an axiom.
Also, we know that, if a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°. It is an axiom. So, given Statement II is true and an axiom.
Thus, in given statements, first is false and second is an axiom.
Hence, given system of axioms is not consistent.
APPEARS IN
संबंधित प्रश्न
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
square
In the following figure, if AC = BD, then prove that AB = CD.
How many least number of distinct points determine a unique line?
In how many points two distinct planes can intersect?
The three steps from solids to points are ______.
The number of dimensions, a surface has ______.
Thales belongs to the country ______.
The statements that are proved are called axioms.
In the following figure BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
The following statement is true or false? Give reason for your answer.
A terminated line can be produced indefinitely on both the sides.
