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 how many points a line, not in a plane, can intersect the plane?
The number of dimensions, a solid has ______.
In ancient India, the shapes of altars used for household rituals were ______.
Thales belongs to the country ______.
Pythagoras was a student of ______.
‘Lines are parallel, if they do not intersect’ is stated in the form of ______.
The boundaries of the solids are curves.
If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AB = BC, BX = BY. Show that AX = CY.
