3. Prove Theorem 3.5 by completing each direction of the biconditional as given sepa- rately in the following two parts. (a) Prove that every point on the perpendicular bisector of a line segment AB is equidistant from the segment's endpoints. (b) Prove that every point that is equidistant from the endpoints of a line segment AB lies on its perpendicular bisector. 4. Prove that the median to the base of an isosceles triangle is perpendicular to the base and bisects the opposite angle.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 6AEXP
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(a) Proposition 1.13
(b) Proposition 1.14
3. Prove Theorem 3.5 by completing each direction of the biconditional as given sepa-
rately in the following two parts.
(a) Prove that every point on the perpendicular bisector of a line segment AB is
equidistant from the segment's endpoints.
(b) Prove that every point that is equidistant from the endpoints of a line segment
AB lies on its perpendicular bisector.
4. Prove that the median to the base of an isosceles triangle is perpendicular to the base
and bisects the opposite angle.
Transcribed Image Text:(a) Proposition 1.13 (b) Proposition 1.14 3. Prove Theorem 3.5 by completing each direction of the biconditional as given sepa- rately in the following two parts. (a) Prove that every point on the perpendicular bisector of a line segment AB is equidistant from the segment's endpoints. (b) Prove that every point that is equidistant from the endpoints of a line segment AB lies on its perpendicular bisector. 4. Prove that the median to the base of an isosceles triangle is perpendicular to the base and bisects the opposite angle.
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