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1) The two column proof for ΔLMN ≅ ΔLON is as developed below.
2) The two column proof for ΔGHJ ≅ ΔKLM is as developed below
A two-column proof is defined as a geometric proof that consists of a list of statements, and then the reasons that we know those statements are deemed to be true.
1) The two column proof showing that ΔLMN ≅ ΔLON is;
Statement 1: LN bisects ∠MLO and LM ≅ LO
Reason 1: Given
Statement 2: MN ≅ ON
Reason 2: Line segment bisector
Statement 3: ∠MLN ≅ ∠OLN
Reason 3: def. of angle bisector
Statement 4: LN ≅ LN
Reason 4: Reflexive property of congruence
Statement 5: ΔLMN ≅ ΔLON
Reason 5: SSS Congruency postulate
2) The two column proof is as follows;
Statement 1: ∠G ≅ ∠K, ∠J ≅ ∠M
Reason 1: Given
Statement 2: ∠H ≅ ∠L
Reason 2: 3rd angle theorem
Statement 4: ΔGHJ ≅ ΔKLM
Reason 4: ASA Congruency Postulate
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