MATH SOLVE

5 months ago

Q:
# The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD. 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? (5 points) 1. Corresponding Angles Theorem 2. Alternate Interior Angles Theorem 1. Alternate Interior Angles Theorem 2. Corresponding Angles Theorem 1. Corresponding Angles Theorem 2. Corresponding Angles Theorem 1. Alternate Interior Angles Theorem 2. Alternate Interior Angles Theorem

Accepted Solution

A:

The incomplete portion is
Angles _____1_________ are congruent by the Alternate Interior Angles Theorem. Angles _____2_________ are congruent by the Corresponding Angles Theorem.
1) <PBC and <BAD
2) <BAT and <CDA
Angles <PBC and <BAD are congruent by the Alternate Interior Angles Theorem. Angles <BAT and <CDA are congruent by the Corresponding Angles Theorem.
<PBC and <BAD are the Alternate Interior Angles of parallel lines AD and BC and traversal is AP
<BAT and <CDA are the Alternate Interior Angles of parallel lines AB and CD and traversal is TD