In this exercise we will practice defining terms. Be careful...

In this exercise we will practice defining terms. Be careful to use only previously defined terms, and take care not to use imprecise and colloquial language in your definitions. (a) Define the term midpoint of a segment. (b) Define the term perpendicular bisector of a segment. (c) Define the tem triangle defined by three non-collinear points $A, B, C$. (d) Define the term equilateral triangle. In the next set of exercises, we consider the logical equivalence of Euclid's fifth postulate with Playfair's Postulate. You may use any of the first 28 Propositions of Euclid (found in Appendix B) and/or any of the results from this section for these exercises.

In this exercise we will practice defining terms. Be careful to use only previously defined terms, and take care not to use imprecise and colloquial language in your definitions.
(a) Define the term midpoint of a segment.
(b) Define the term perpendicular bisector of a segment.
(c) Define the tem triangle defined by three non-collinear points $A, B, C$.
(d) Define the term equilateral triangle.
In the next set of exercises, we consider the logical equivalence of Euclid's fifth postulate with Playfair's Postulate. You may use any of the first 28 Propositions of Euclid (found in Appendix B) and/or any of the results from this section for these exercises.

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Key Concepts

Midpoint

In Euclidean geometry, the midpoint of a segment is the point that divides the segment into two congruent parts; that is, each of the resulting segments has the same length. This concept is fundamental in constructions and proofs where equal partitioning of a line segment is required.

Perpendicular Bisector

The perpendicular bisector of a segment is a line (or ray) that both passes through the midpoint of the segment and forms right angles (90°) with it. This concept is critical in geometric constructions and in proving properties related to congruence and symmetry.

Triangle

A triangle is a polygon formed by three non-collinear points connected by segments, which serve as its sides. The criterion of non-collinearity ensures that the points do not lie on a single straight line, which guarantees the enclosed area that characterizes a triangle.

Equilateral Triangle

An equilateral triangle is a special type of triangle in which all three sides are congruent. This congruence of sides implies that all the internal angles are also congruent, making the shape highly symmetric and a frequent subject in both theoretical and applied geometry.

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