Euclid's Geometry Quiz

What does the first axiom of Euclid's geometry state?

• The whole is greater than the part.

• Things which are equal to the same thing are equal to one another.

• If equals are added to equals, the wholes are equal.

• If equals are subtracted from equals, the remainders are equal.

In the context of the first axiom, if triangle ABC is equal to triangle PQR, and triangle XYZ is equal to triangle PQR, what can be concluded?

• Triangle ABC is not equal to triangle XYZ.

• Triangle ABC is equal to triangle XYZ.

• Triangle XYZ is larger than triangle ABC.

• Triangle PQR is not equal to triangle XYZ.

According to the second axiom, what happens when equals are added to equals?

• The wholes are not equal.

• The wholes are equal.

• The wholes become smaller.

• The wholes become larger.

If 5 is equal to 5 and 2 is equal to 2, what is the result when both are added according to the second axiom?

• The result is 9.

• The result is 8.

• The result is 7.

• The result is 6.

What does the third axiom of Euclid's geometry state?

• If equals are subtracted from equals, the remainders are equal.

• If equals are added to equals, the wholes are equal.

• Things which coincide with one another are equal to one another.

• The whole is greater than the part.

In the third axiom, if 5 minus 2 equals 3, what is the result of subtracting 2 from another 5?

• The result is 5.

• The result is 4.

• The result is 3.

• The result is 2.

What does it mean when two shapes coincide according to Euclid's axioms?

• They are smaller.

• They are larger.

• They are equal.

• They are different.

According to Euclid, what is true about the whole compared to its part?

• The whole is greater than the part.

• The whole is smaller than the part.

• The whole is equal to the part.

• The whole is unrelated to the part.

If a line segment AB is 5 units and CD is also 5 units, what can be said about their doubles according to Euclid's axioms?

• Their doubles are not equal.

• Their doubles are equal.

• Their doubles are smaller.

• Their doubles are unrelated.

What happens to two equal objects when they are halved according to Euclid's axioms?

• Their halves become unrelated.

• Their halves are not equal.

• Their halves are equal.

• Their halves become larger.