Question

NEED HELP ASAP!!!

Fill in the missing statement and reason in the proof of the Alternate Interior Angles Theorem.

Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.

It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. ∠AGF and ∠EGB are vertical and congruent by the Vertical Angles Theorem. ∠EGB and ∠EHD are congruent according to the ________. Finally, ________ by the Transitive Property of Equality.

Group of answer choices

A. Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent

B. Alternate Exterior Angles Theorem; ∠EGB and ∠EHD are congruent

C. Corresponding Angles Theorem; ∠EGB and ∠EHD are congruent

D. Alternate Exterior Angles Theorem; ∠AGF and ∠EHD are congruent

Answer 1

In the proof of the Alternate Interior Angles Theorem, ∠EGB and ∠EHD are congruent because of the Corresponding Angles Theorem, which ultimately shows that ∠AGF and ∠EHD are congruent by the Transitive Property of Equality. Therefore correct option is A

Step-by-step explanation:

The question asks us to complete the proof of the Alternate Interior Angles Theorem. Given that segment AB is parallel to segment CD and transversal EF intersects them at points G and H respectively, angle AGF and angle EGB are congruent due to the Vertical Angles Theorem. Now, to fill in the missing parts of the proof, let's look at the options provided.

Since AB is parallel to CD and EF is a transversal, angle EGB and angle EHD are congruent because of the Corresponding Angles Theorem. By the Transitive Property of Equality, if angle AGF is congruent to angle EGB, and angle EGB is congruent to angle EHD, then angle AGF must be congruent to angle EHD.

Therefore, the correct answer is:

Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent