Provide an Analytic Proof for each of the following theorems.The medians of an equilateral triangle are altitudes.If M is the middle point of the side AB of the parallelogram ABCD, then the line segment MC and the diagonal BD trisect each other.The line joining the midpoints of the nonparallel sides of a trapezoid is parallel to the parallel sides and has length equal to one-half the sum of the lengths of the parallel sides.If the sum of the squares of two sides of a triangle equals the square of the third side, then the triangle is a right triangle.The perpendicular bisector of a chord of a circle contains the center.

Steps of solution Part 1) Proof:Let's place an equilateral triangle △ABC on the coordinate plane…

Answered: Provide an Analytic Proof for each of…

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Provide an Analytic Proof for each of the following theorems.

The medians of an equilateral triangle are altitudes.
If M is the middle point of the side AB of the parallelogram ABCD, then the line segment MC and the diagonal BD trisect each other.
The line joining the midpoints of the nonparallel sides of a trapezoid is parallel to the parallel sides and has length equal to one-half the sum of the lengths of the parallel sides.
If the sum of the squares of two sides of a triangle equals the square of the third side, then the triangle is a right triangle.
The perpendicular bisector of a chord of a circle contains the center.