please explain in simple language
1) Euclid's 4th axiom that states : things which coincide with one another are equal to one another
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Things that coincide with one another
are equal to one another.
This means that if we have two triangles, ABC, DEF, say, and if we

could place them one on the other; and if AB were to coincide with DE, and BC with EF, and CA with FD, then we could conclude that those triangles were equal to one another in all respects. Their respective angles would be equal, and the triangles themselves would be equal areas. When figures would coincide in that way, we say that they are congruent.
Axiom 4 therefore states a sufficient condition for equality, namely congruence. That is obvious; that is why it is an axiom.
If we can show, then, that two triangles are congruent, we will know the following:
1) Their corresponding sides are equal.
2) Their corresponding angles are equal.
3) They are equal areas.
Those are the three magnitudes of plane geometry: length (the sides), angle, and area. Congruence is our first way of knowing that magnitudes of the same kind are equal.
What are sufficient conditions, then, for triangles to be congruent?
Side-angle-side

The fundamental condition for congruence is that two sides and the included angle of one triangle be equal to two sides and the included angle of the other.
Euclid proved this by supposing one triangle actually placed on the other, and allowing the equal sides and equal angles to coincide. He then argued that the remaining sides must also coincide. (You might perform this mental experiment yourself.) This is called proof by superposition. And it is out of favor these days. It was even called into question in Euclid's time -- why not prove every theorem by superposition?
If superposition, then, is the only way to see the truth of a proposition, then that proposition ranks with our basic understanding; it is a kind of mental, experimental result. Therefore it should be a first principle, not a theorem.
Nowadays, this proposition is accepted as a postulate. We shall not prove it either.
please mark this as brainliest answer
are equal to one another.
This means that if we have two triangles, ABC, DEF, say, and if we

could place them one on the other; and if AB were to coincide with DE, and BC with EF, and CA with FD, then we could conclude that those triangles were equal to one another in all respects. Their respective angles would be equal, and the triangles themselves would be equal areas. When figures would coincide in that way, we say that they are congruent.
Axiom 4 therefore states a sufficient condition for equality, namely congruence. That is obvious; that is why it is an axiom.
If we can show, then, that two triangles are congruent, we will know the following:
1) Their corresponding sides are equal.
2) Their corresponding angles are equal.
3) They are equal areas.
Those are the three magnitudes of plane geometry: length (the sides), angle, and area. Congruence is our first way of knowing that magnitudes of the same kind are equal.
What are sufficient conditions, then, for triangles to be congruent?
Side-angle-side

The fundamental condition for congruence is that two sides and the included angle of one triangle be equal to two sides and the included angle of the other.
Euclid proved this by supposing one triangle actually placed on the other, and allowing the equal sides and equal angles to coincide. He then argued that the remaining sides must also coincide. (You might perform this mental experiment yourself.) This is called proof by superposition. And it is out of favor these days. It was even called into question in Euclid's time -- why not prove every theorem by superposition?
If superposition, then, is the only way to see the truth of a proposition, then that proposition ranks with our basic understanding; it is a kind of mental, experimental result. Therefore it should be a first principle, not a theorem.
Nowadays, this proposition is accepted as a postulate. We shall not prove it either.
please mark this as brainliest answer
ambysensei:
thank you so much
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