# ma722_unit2_section3_discussion.pdf - Stan Oleynik...

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Stan Oleynik Assignment 3 - Unit 2 Section 3 Assignment Discussion - Problem 2-a on page 65 MA 722 Spring 2019 Statement: Prove theorem 48 for a.) Fig III, 22. Theorem 48: The line joining the midpoints of two sides of a triangle is parallel to the line containing the third side, having a common perpendicular with it, and the segment joining the midpoints is less than half of the third side. Proof: Let’s prove that BC || HG and there is a common perpendicular: 1. From the textbook, page 63, we proved that 4 ADF = 4 BDG , 4 AFE = 4 CHE , and thus BG = AF = HC 2. By construction of line DE and quadrilateral BCHG , we have that