Choose one of the following statements to complete the sentence. Discuss your reasoning for your selection.
Euclid’s treatment of the fifth axiom...
A) ... shows that it is important to question the nature of the assumptions that are made.
B) ... is now known to be wrong.
C) ... shows that he was really smart.
7. Name the geometry in which the statement is possible.
The base angles of a Saccheri quadrilateral are acute.
the maturity vale of a five-month loan of 1,500 is 1,583. find the simple annual interest rate to the nearest hundredth
13.28%
1) Euclid’s treatment of the fifth axiom... A) ... shows that it is important to question the nature of the assumptions that are made.
Reasoning: Euclid's treatment of the fifth axiom, also known as the parallel postulate, can be seen in his book "Elements." In this work, Euclid attempts to prove the parallel postulate using other axioms and theorems. His efforts to justify this particular assumption indicate the importance he placed on critically examining the assumptions made in geometry. This aligns with the statement that his treatment of the fifth axiom shows the significance of questioning the nature of assumptions.
2) The base angles of a Saccheri quadrilateral are acute.
In hyperbolic geometry, the base angles of a Saccheri quadrilateral are acute.
Reasoning: In Euclidean geometry, a Saccheri quadrilateral is a quadrilateral with two equal sides and two right angles. However, in hyperbolic geometry, which is non-Euclidean, a Saccheri quadrilateral is formed on a hyperbolic plane, where the angles of a quadrilateral can differ from those in Euclidean geometry. In hyperbolic geometry, the base angles of a Saccheri quadrilateral are acute, meaning they are less than 90 degrees.