Pre-Calculus Homework Solutions 112

# Pre-Calculus Homework Solutions 112 - 28. Given: ABC S is...

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28. Given: n ABC S is the midpoint of A w C w . T is the midpoint of B w C w . Prove: ST 5 } 1 2 } AB Midpoint S is 1 } b 1 2 0 } , } c 1 2 0 } 2 or 1 } b 2 } , } 2 c } 2 . Midpoint T is 1 } a 1 2 b } , } 0 1 2 c } 2 or 1 } a 1 2 b } , } 2 c } 2 . Proof: ST 5 ¬ ! 1 } a 1 2 b } § 2 } b 2 } 2 2 § 1 1 } 2 c } § 2 } 2 c } 2 2 § 5 ¬ ! 1 } a 2 } 2 2 1 § 0 2 § 5 ¬ ! 1 } a 2 } 2 2 § or } a 2 } AB 5 ¬ Ï ( a 2 0 w ) 2 1 (0 w 2 0) 2 w 5 ¬ Ï a 2 1 0 w 2 w or a ST 5 ¬ } 1 2 } AB 29. Given: n ABD , n FBD AF 5 6, BD 5 3 Prove: n ABD > n FBD Proof: B w D w > ¬ B w D w by the Reflexive Property. AD 5 ¬ Ï (3 2 0 w ) 2 1 (1 w 2 1) 2 w 5 Ï 9 1 0 w or 3 DF 5 ¬ Ï (6 2 3 w ) 2 1 (1 w 2 1) 2 w 5 Ï 9 1 0 w or 3 Since AD 5 DF , A w D w > D w F w . AB 5 Ï (3 2 0 w ) 2 1 (4 w 2 1) 2 w 5 Ï 9 1 9 w or 3 Ï 2 w BF 5 Ï (6 2 3 w ) 2 1 (1 w 2 4) 2 w 5 Ï 9 1 9 w or 3 Ï 2 w Since AB 5 BF , A w B w > B w F w . n ABD > n FBD by SSS. 30. Given:
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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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