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

Question

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olayemiolakunle65 olayemiolakunle65 · Answer 1 · 2020-10-11T03:03:19+02:00

Answer:

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)

vintechnology vintechnology · Answer 2 · 2022-03-30T14:25:48+02:00

∠1 and ∠2 are alternate interior angles .

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. Alternate interior angles are congruent. Therefore,

∠2 ≅ ∠3 (alternate interior angles)

Since line LM is parallel to line NO, ∠1 and ∠2 are alternate interior angles.

Therefore,

∠1 ≅∠2 (alternate interior angles)

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