Given:
LM = LN, KM = KN, KO bisects angle MKN
What we want to prove:
LO bisects angle MLN
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Proof:
Statement 1: KM = KN
Reason 1: Given
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Statement 2: KO bisects angle MKN
Reason 2: Given
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Statement 3: Angle MKO = Angle NKO
Reason: Definition of angle bisection
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Statement 4: KO = KO
Reason 4: Reflexive property of congruence
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Statement 5: Triangle MKO = Triangle NKO
Reason 5: SAS postulate
note: this combines statements 1, 3, and 4 (for the "S", "A", and "S" in that order)
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Statement 6: MO = ON
Reason 6: CPCTC
note: CPCTC stands for "corresponding parts of congruent triangles are congruent"
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Statement 7: Angle KOM = Angle KON
Reason: CPCTC
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Statement 8: OL = OL
Reason 8: Reflexive property of congruence
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Statement 9: Triangle MOL = Triangle NOL
Reason 9: SAS postulate
note: used statements 6, 7, 8 for the "S", "A", "S" in that order
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Statement 10: Angle MLO = Angle NLO
Reason 10: CPCTC
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Statement 11: LO bisects angle MLN
Reason 11: Definition of angle bisection
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That concludes the proof. We did not use the statement "LM = LN", so it is unnecessary.
