Complete the proof that the opposite angles of a parallelogram are congruent as a paragraph proof. Glven: ABCD is a parallelogram. Prove: ZA = 2C (a similar proof shows that ZB – ZD).
B.
It is given that ABCD is a parallelogram, so AB || (select) v and AD || (select) by the definition of a
parallelogram. Since two points determine a line, you can draw DB. DB = (select)y by the Reflexive
Property of Congruence. By the Alternate Interior Angles Theorem, ZADB < (select) and
ZABD = (select). You can conclude that AABD = (select) by the ASA Triangle Congruence
Theorem, and so, ZA – 4 (select)y by CPCTC.