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# What is the law of detachment in geometry?

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In geometry, the law of detachment is a form of deductive reasoning in which two premises in relation to the same subject are examined to come to a reasonable conclusion. This law considers a hypothesis made with regard to a statement and uses deductive reasoning to find a true answer.

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The "if" part of the law of deductive reasoning is always a hypothesis or a reasoned guess. The statement made after "then" is the conclusion. This is also referred to as a conditional statement. The hypothesis must be proven to be true in order for the conclusion to be true as well. Another example of the law of deductive reasoning would be:

• All mammals have fur
• All cats have fur
• All cats must be mammals

If the conclusion is false and the hypothesis is true in a conditional statement, then the conditional statement itself is false. A converse statement in the law of detachment happens when the hypothesis and the conditional statement are reversed. In the given example, the conclusion that all cats must be mammals would remain true.

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## Related Questions

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A median is a line segment that joins any vertex of a triangle to the midpoint of the opposite side of the triangle. A triangle has three sides and three vertices. Hence, it has three medians. A median divides a triangle into two equal halves of equal area.

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In geometry, converse, inverse and contrapositive are conditional statements consisting of a hypothesis and a conclusion. These statements are also known as “if-then statements.” The hypothesis part of a conditional statement is the “if," and the “then” part is the conclusion. The conclusion is the result of a hypothesis.

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The inventor of geometry was Euclid, and his nickname was The Father of Geometry. Euclid obtained his education at Plato's Academy in Athens, Greece and then moved to Alexandria.

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Spherical geometry is the branch of mathematics that deals with figures placed on the surface of a sphere. It can also be defined as a three-dimensional view of more traditional planar geometry; although, there are numerous differences between the planar and spherical subsets of geometrical study. Some of the basic tenets of planar geometry don't carry over to spherical geometry because it deals with different mathematical concepts.