Given: NM || PO and Angle 1 is congruent To angle 3 Prove: LM || NO

Given
Transitive property
Alternate interior angle theorem
Converse alternate interior angle theorem

i. LM || NO  (converse alternate interior angle theorem)

ii. <1 ≅ <2    (alternate interior angle theorem)

Step-by-step explanation:

Two or more lines are said to be parallel if they do not meet when extended, even till infinity.

Alternate angles are said to be equal in measure.

Given that;

<1 ≅ < 3,

Since <2 ≅ <3 (alternate interior angle theorem)

Then,

<1 ≅ <2 (transitive property)

Also,

<1 ≅ <2 (alternate interior angle theorem)

Therefore since <1 ≅ <2, thus;

LM || NO (converse alternate interior angle theorem)

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step-by-step explanation: