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.
In how many points a line, not in a plane, can intersect the plane?
How many planes can be made to pass through a line and a point not on the line?
How many planes can be made to pass through two points?
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
Solve the following question using appropriate Euclid’s axiom:
It is known that x + y = 10 and that x = z. Show that z + y = 10?
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have BX = `1/2` AB, BY = `1/2` BC and AB = BC. Show that BX = BY.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
The following statement is true or false? Give reason for your answer.
If two circles are equal, then their radii are equal.
