SOLUTION: given: ABCD is a parallelogram prove: < A congruent to < C, < B congruent to < D

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Question 411716: given: ABCD is a parallelogram
prove: < A congruent to < C, < B congruent to < D
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

given: ABCD is a parallelogram 
prove: < A congruent to < C, < B congruent to < D



Draw diagonal BD




AB parallel to CD                   opposite sides of a parallelogram

angle ABD congruent to angle CDB    alternate interior angles when transversal
                                    BD cut parallel lines AB and CD

AD parallel to CB                   opposite sides of a parallelogram

angle ADB congruent to angle CBD    alternate interior angles when transversal
                                    BD cuts parallel lines AD and CB

BD is congruent to itself

triangle ABD congruent to CDB       Angle Side Angle

Angle A congruent to angle C

Angle ADB + Angle CDB is congruent to
Angle CBD + Angle ABD                   Sums of Congruent angles are Congruent

Angle ADC is congruent to Angle ABD      A whole angle is equal to
                                         the sum of its parts

Edwin