MATH SOLVE

4 months ago

Q:
# Prove LO bisects angle MLN and identify which given statement is unnecessary.β

Accepted Solution

A:

Given:LM = LN, KM = KN, KO bisects angle MKNWhat we want to prove:LO bisects angle MLN=====================================Proof:Statement 1: KM = KNReason 1: Given---------------------Statement 2: KO bisects angle MKNReason 2: Given---------------------Statement 3: Angle MKO = Angle NKOReason: Definition of angle bisection---------------------Statement 4: KO = KOReason 4: Reflexive property of congruence---------------------Statement 5: Triangle MKO = Triangle NKOReason 5: SAS postulatenote: this combines statements 1, 3, and 4 (for the "S", "A", and "S" in that order)---------------------Statement 6: MO = ONReason 6: CPCTCnote: CPCTC stands for "corresponding parts of congruent triangles are congruent"---------------------Statement 7: Angle KOM = Angle KONReason: CPCTC---------------------Statement 8: OL = OLReason 8: Reflexive property of congruence---------------------Statement 9: Triangle MOL = Triangle NOLReason 9: SAS postulatenote: used statements 6, 7, 8 for the "S", "A", "S" in that order---------------------Statement 10: Angle MLO = Angle NLOReason 10: CPCTC---------------------Statement 11: LO bisects angle MLNReason 11: Definition of angle bisection---------------------That concludes the proof. We did not use the statement "LM = LN", so it is unnecessary.