Pre-Calculus Homework Solutions 245

Pre-Calculus Homework Solutions 245 - 43. Given: Prove: M...

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247 Chapter 8 43. Given: ~ MNPQ / M is a right angle. Prove: / N , / P and / Q are right angles Proof: By definition of a parallelogram, M w N w i Q w P w . Since / M is a right angle, M w Q w ' M w N w .By the Perpendicular Transversal Theorem, M w Q w ' Q w P w . / Q is a right angle, because perpendicular lines form a right angle. / N > / Q and / M > / P because opposite angles in a parallelogram are congruent. / P and / N are right angles, since all right angles are congruent. 44. Given: ACDE is a parallelogram. Prove: E w C w bisects A w D w . A w D w bisects E w C w . Proof: It is given that ACDE is a parallelogram. Since opposite sides of a parallelogram are congruent, E w A w > D w C w .By definition of a parallelogram, E w A w i D w C w . / AEB > / DCB and / EAB > / CDB because alternate interior angles are congruent. n EBA > n CBD by ASA. E w B w > B w C w and A w B w > B w D w by CPCTC. By the definition of segment bisector, E w C w bisects A w D w and A w D w bisects E w C w .
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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