Question

The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent:


According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the ____________. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the _____________. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent. What theorems accurately complete the proof?

A) Corresponding Angles Theorem
     Alternate Interior Angles Theorem



B) Alternate Interior Angles Theorem
    Corresponding Angles Theorem

C) Corresponding Angles Theorem
     Corresponding Angles Theorem

D) Alternate Interior Angles Theorem
     Alternate Interior Angles Theorem

Answer 1

;))

Explanation:

rat

Answer 2

For a better understanding of the answer to the question provided here kindly check the diagram that has been attached here.

The attached diagram has the complete construction details as has been asked to do in the question.

Let us now begin answering.

As can be clearly seen from the attached diagram angles PBC and BAD are congruent by the Corresponding Angles Theorem AB acts as the transversal for the lines BC and AD which are parallel.

Also, it can be clearly seen that the angles ABC and BAT are congruent by the Alternate Interior Angles Theorem as AB acts as the transversal for the lines BC and TAD which are parallel.

Thus, the only option from the given list of options which matches the answer is Option A.

Thus, Option A is the correct option and thus the final answer.