Question

The question has to do with finding the proven with the given and I’m not sure what to do

Answer 1

The reason for ∠8 ≅ ∠4 is alternate exterior angles

The question has to do with finding the proven with the given.

We have been given line f is parallel to line g.

We need to prove angle 8 is congruent to angle 4.

From given figure we observe that line f || line g and these parallel lines are intersected by a transversal.

And the angle 8 are angle 4 are alternate exterior angles.

We know that alternate exterior angles are congruent.

so, ∠8 ≅ ∠4

Therefore, the reason for ∠8 ≅ ∠4 is alternate exterior angles

Learn more about alternate exterior angles here:

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Answer 2

Using the two parallel line theorems we proved that ∠8 ≅ ∠4.

In the given question,

Given: f || g

Prove: ∠8 ≅ ∠4

We using given diagram in proving that ∠8 ≅ ∠4

Since f || g, by the Corresponding Angles Postulate which states that "When a transversal divides two parallel lines, the resulting angles are congruent." So

∠8≅∠6

Then by the Vertical Angles Theorem which states that "When two straight lines collide, two sets of linear pairs with identical angles are created."

∠6≅∠4

Then, by the Transitive Property of Congruence which states that "All shapes are congruent to one another if two shapes are congruent to the third shape."

∠8 ≅ ∠4

Hence, we proved that ∠8 ≅ ∠4.

To learn more about parallel line theorems link is here

brainly.com/question/27033529

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