Pre-Calculus Homework Solutions 106

Pre-Calculus Homework Solutions 106 - 27 LMN is equilateral...

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27. n LMN is equilateral, so L w M w> M w N w > L w N w . M w P w bisects L w N w , so M w P w bisects / LMN . n LMN is equilateral, hence equiangular. So m / LMN 5 m / MLP 5 60 and m / PML 5 30. LM 5 ¬ MN 3 x 1 1 5 ¬ 4 x 2 2 3 5 ¬ x m / PLM 1 m / PML 1 m / MPL 5 ¬ 180 60 1 30 1 5 y 5 ¬ 180 90 1 5 y 5 ¬ 180 5 y 5 ¬ 180 y 5 ¬ 18 28. LM 5 3 x 1 1 5 3(3) 1 1 or 10 LM 5 MN 5 LN , so all sides have measure 10. 29. Given: n XKF is equilateral. X w J w bisects / X . Prove: J is the midpoint of K w F w . Proof: 30. Given: n MLP is isosceles. N is the midpoint of M w P w . Prove: L w N w ' M w P w Proof: 31. Case I: Given: n ABC is an equilateral triangle. Prove: n ABC is an equiangular triangle. Proof: Case II: Given: n ABC is an equiangular triangle. Prove: n ABC is an equilateral triangle. Proof: AC B B MP N L KF J X 1 2 Chapter 4 108 Statements Reasons 1. n XKF is equilateral. 1. Given 2. K w X w > F w X w 2. Definition of equilateral n 3. / 1 > / 2 3. Isosceles Triangle Theorem 4. X w J w bisects / X 4. Given 5. / KXJ > / FXJ 5. Def. of / bisector 6. n KXJ > n FXJ 6. ASA 7. K w J w > J w F w 7. CPCTC 8. J
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