Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
The following statement is true or false? Give reason for your answer.
Only one line can pass through a single point.
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.)
How many least number of distinct points determine a unique line?
In how many lines two distinct planes can intersect?
In ancient India, the shapes of altars used for household rituals were ______.
Euclid belongs to the country ______.
‘Lines are parallel, if they do not intersect’ is stated in the form of ______.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
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.
If two circles are equal, then their radii are equal.
