Because of his habit of always peeking into the books of higher grades, Ted was able to recollect that Euclid gave some axioms. How many axioms did Euclid give?
Because of his habit of always peeking into the books of higher grades, Ted was able to recollect that Euclid gave some axioms. How many axioms did Euclid give?
The correct option is D 5
Euclid gave 5 axioms. Euclid’s 5 axioms are:
1. Things which are equal to the same thing are also equal to one another.
If a = b and b = c, then a = b.
2. If equals be added to equals, the wholes are equal.
This basically means this:
If a = b, then a + c = b + c.
3. If equals be subtracted from equals, the remainders are equal.
This is similar to the second axiom. This tells that:
If a = b, then a – c = b – c.
4. Things which coincide with one another are equal to one another.
Two things which are exactly alike are equal. For e.g. two triangles are congruent, they coincide with each other. There sides, angles, perimeter, area, all are equal.
5. The whole is greater than the part.
This means that x + a > x.
All the other theorems in geometry are derived from these 5 axioms.
5
Euclid gave 5 axioms. Euclid’s 5 axioms are:
1. Things which are equal to the same thing are also equal to one another.
If a = b and b = c, then a = b.
2. If equals be added to equals, the wholes are equal.
This basically means this:
If a = b, then a + c = b + c.
3. If equals be subtracted from equals, the remainders are equal.
This is similar to the second axiom. This tells that:
If a = b, then a – c = b – c.
4. Things which coincide with one another are equal to one another.
Two things which are exactly alike are equal. For e.g. two triangles are congruent, they coincide with each other. There sides, angles, perimeter, area, all are equal.
5. The whole is greater than the part.
This means that x + a > x.
All the other theorems in geometry are derived from these 5 axioms.
