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Two angles which are on opposite sides of the transversal and between the parallel lines and do not share the same vertex. They are congruent.

User Given
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1 Answer

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Answer:

Interior angles are congruent.

Explanation:

We see that angles 3,4,5,6 are between the two parallel lines . These angles are called interior angles.

Angles 3,6 are opposite and do not share the same vertex.

Similarly angles 4 and 5 do not share the same vertex.

They are congruent.

If we look closely we see that angles 3 &4 and angles 5&6 are supplementary angles.

i.e they together make up the 180 degrees on the straight line.

On the outer sides of the parallel lines angles 1&2 and angles 7 & 8 are exterior angles

which also make supplementary angles on the parallel lines.

From the diagram we see that

∠ 5= ∠7

and

∠6 = ∠ 8

as the corresponding angles are equal

∠8=∠3

∠7=∠4

As they are opposite angles

Similarly

∠1=∠6

∠2=∠5 ( opposite angles)

From above

∠5=∠7

but ∠7= ∠4

therefore

∠ 5= ∠4-----------------A

Also

∠6 = ∠ 8

but ∠8=∠3

therefore

∠6=∠8----------------------B

From An and B we conclude interior angles are congruent

Two angles which are on opposite sides of the transversal and between the parallel-example-1
User Audiophile
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