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
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 lines can intersect?
The three steps from solids to points are ______.
The number of dimensions, a surface has ______.
Thales belongs to the country ______.
‘Lines are parallel, if they do not intersect’ is stated in the form of ______.
The things which are double of the same thing are equal to one another.
The statements that are proved are called axioms.
Solve the following question using appropriate Euclid’s axiom:
Look at the figure. Show that length AH > sum of lengths of AB + BC + CD.
