Given that ABCD is a parallelogram, prove ZB = LD.
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Alternate Interior Angles Theoghm
Substitution
Statements
Reasons
ABCD is a parallelogram
Given
AB = DC and BC = AD
Definition of a parallelogram
mLA + mLB = 180° and mLA + m<D = 180°
Same Side Interior Angles Theorem
mLA + mLB = mLA + m<D
mLB = mLD
LBE LD
Angles with the same measure are congruent
Corresponding Angles Theorem
Multiplicative Property of Equality
AB || DC and BC || AD
Subtraction Property of Equality
mLB = mLD
Corresponding Angles Theorem
Therefore, ZB = LD.