Question

given: ( abcd ) is a parallelogram and ( angle a cong angle e ).
prove: ( overline{cd} cong overline{ce} ).
step
1
2
3
4
5
statement
( abcd ) is a parallelogram
( angle a cong angle e )
( overline{ba} parallel overline{cd} )
( angle a cong angle cde )
type of statement
( overline{cd} cong overline{ce} )
reason
given
opposite sides of a parallelogram are parallel
parallel lines cut by a transversal form congruent corresponding angles
in a triangle, sides opposite of congruent angles are congruent

Explanation:

Step1: Substitute angles

Since \(\angle A\cong\angle E\) (given) and \(\angle A\cong\angle CDE\) (from step 3), by the transitive property of congruence, \(\angle E\cong\angle CDE\).

Answer:

\(\angle E\cong\angle CDE\)