Statement | Reason
0. LM≅NO Given
,
1. ∠LMO≅∠NOM ,Given
,
2. ∠LOM≅∠NMO ,Corresponding angles are congruent
,
3. MO≅OM ,Reflexive Property
,
4. ∠L≅∠O ,Corresp. parts of congruent triangles are congruent
,
5. Δ LMO≅ΔNOM ,Angle Angle Side Congruence
1) In order to write proofs in geometry, let's start with it is already given and then making use of our knowledge proceed with the steps
2) So let's begin with the first lines
Statement | Reason
LM≅NO Given
∠LMO≅∠NOM Given
Having these, we can state that there are parallel lines, and then apply the properties of two parallel lines intercepted by a transversal one. So let's continue:
Statement | Reason
LM≅NO Given
∠LMO≅∠NOM Given
∠LOM≅∠NMO Corresponding angles are congruent
MO≅OM Reflexive Property
Note that if LM and NO are congruent and the angles ∠LMO≅∠NOM are congruent as well then we have two parallel lines. So, it's safe to state that ∠LOM≅∠NMO is also congruent because they are corresponding angles.
Note that any line segment is congruent to itself, that's what the Reflexive Property states.
3) Let's continue to the last part of it. All that's left to prove that both triangles are congruent is to prove that ∠L and ∠M are also congruent.
If 2 out of three angles from Δ LMO are congruent to the corresponding angles of ΔNOM then we can write out the following statement #5
Statement | Reason
0. LM≅NO Given
,
1. ∠LMO≅∠NOM ,Given
,
2. ∠LOM≅∠NMO ,Corresponding angles are congruent
,
3. MO≅OM ,Reflexive Property
,
4. Δ LMO≅ΔNOM ,Angle Side Angle Congruence
Statement | Reason
0. LM≅NO Given
,
1. ∠LMO≅∠NOM ,Given
,
2. ∠LOM≅∠NMO ,Corresponding angles are congruent
,
3. MO≅OM ,Reflexive Property
,
4. Δ LMO≅ΔNOM ,Angle Side Angle Congruence