Euclid Geometry Flashcards
What are axioms in the context of Euclidean geometry?
Assumptions considered to be universal truths that are not proven.
State the first axiom of Euclidean geometry.
Things that are equal to the same thing are equal to each other.
What does the second axiom of Euclidean geometry state?
If equals are added to equals, the wholes are equal.
What is the third axiom of Euclidean geometry?
The whole is greater than the part.
State the fourth axiom of Euclidean geometry.
If equals are subtracted from equals, the remainders are equal.
What is a postulate in Euclidean geometry?
A statement accepted as true without proof.
What does the first postulate of Euclidean geometry state?
Things that coincide with each other are equal to each other.
What does the second postulate of Euclidean geometry allow?
A finite straight line can be extended continuously in a straight line.
According to Euclidean geometry, what can be drawn between any two points?
A straight line.
What is the significance of the third postulate in Euclidean geometry?
A circle can be drawn with any center and any radius.
What are axioms in the context of Euclidean geometry?
Assumptions considered to be universal truths that are not proven.
State the first axiom of Euclidean geometry.
Things that are equal to the same thing are equal to each other.
What does the second axiom of Euclidean geometry state?
If equals are added to equals, the wholes are equal.
What is the third axiom of Euclidean geometry?
The whole is greater than the part.
State the fourth axiom of Euclidean geometry.
If equals are subtracted from equals, the remainders are equal.
What is a postulate in Euclidean geometry?
A statement accepted as true without proof.
What does the first postulate of Euclidean geometry state?
Things that coincide with each other are equal to each other.
What does the second postulate of Euclidean geometry allow?
A finite straight line can be extended continuously in a straight line.
According to Euclidean geometry, what can be drawn between any two points?
A straight line.
What is the significance of the third postulate in Euclidean geometry?
A circle can be drawn with any center and any radius.
