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
If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)
Euclid divided his famous treatise “The Elements” into ______.
Boundaries of solids are ______.
A pyramid is a solid figure, the base of which is ______.
In ancient India, the shapes of altars used for household rituals were ______.
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is ______.
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for ______.
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.
