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 Corresponding Angles Theorem. By the __________ Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the Alternate Interior Theorem. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the __________ Property of Equality,∠ABC is congruent to∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.
By the Transitive Property of Equality, we can conclude that angles BCD and BAD are congruent. Additionally, by the Transitive Property of Equality, we can conclude that angles ABC and CDA are congruent. Therefore, the property of equality that is used in both cases is the Transitive Property of Equality. This property states that if a = b and b = c, then a = c. In this case, we use the property to conclude that if angles BCD is congruent to BAD, and angles BAD is congruent to CDA, then angles BCD is congruent to CDA.
