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Pre-Calculus Homework Solutions 245

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

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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, MN QP . Since M is a right angle, MQ MN . By the Perpendicular Transversal Theorem, MQ QP . 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: EC bisects AD . AD bisects EC . Proof: It is given that ACDE is a parallelogram. Since opposite sides of a parallelogram are congruent, EA DC . By definition of a parallelogram, EA DC . AEB DCB and EAB CDB because alternate interior angles are congruent. EBA CBD by ASA. EB BC and AB BD by CPCTC. By the definition of segment bisector, EC bisects AD and AD bisects EC . 45. Given: WXYZ Prove: WXZ YZX Proof: 46. Given: DGHK is a parallelogram. FH GD DJ HK Prove: DJK HFG Proof: 47. Given: BCGH , HD FD Prove: F GCB Proof: 48. MSR PST because they are vertical angles.
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