Pre-Calculus Homework Solutions 160

# Pre-Calculus Homework Solutions 160 - 5 A D and B ABC DEF...

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5. / A > / D and / B > / E , so by AA Similarity, n ABC , n DEF . } D AB E } 5 ¬ } B E C F } } x 2 x 4 } 5 } 5 3 } 3 x 5 ¬ 5( x 2 4) 3 x 5 ¬ 5 x 2 20 2 2 x 5 ¬ 2 20 x 5 ¬ 10 AB 5 x 5 10 DE 5 x 2 4 5 10 2 4 or 6 6. Triangles EFD and BCA are right triangles. To determine whether corresponding sides are proportional, find AB . ( AB ) 2 5 ¬ ( AC ) 2 1 ( BC ) 2 ( AB ) 2 5 ¬ 10 2 1 5 2 5 100 1 25 AB 5 ¬ Ï 125 w or 5 Ï 5 w } D AB E } 5 ¬ } 5 Ï 8 5 w } and } B E C F } 5 } 4 5 } } 5 Ï 8 5 w } Þ } 4 5 } , so the triangles are not similar because corresponding sides are not proportional. 7. If the measures of the corresponding sides are proportional, then the triangles are similar. } D AB F } 5 } 9 3 } or 3, } D AC E } 5 or 3, } B FE C } 5 } 2 7 1 } or 3 } D AB F } 5 } D AC E } 5 } B FE C } , so by SSS Similarity, n DEF , n ACB . 8. Triangles ABC and EDF are isosceles triangles because they each have a pair of congruent sides. Base angles of isosceles triangles are congruent,
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