Question

complete the statements to prove that ( overline{ab} cong overline{cd} ) and ( overline{bc} cong overline{ad} ).

	reason
	definition of a parallelogram
al that intersects two pairs of parallel	drawing a line segment
( overline{bc} ).
( angle a cong angle cad )	alternate interior angles theorem
( angle bca = mangle cad )
	congruent angles have equal measures. alternate interior angles theorem alternate exterior angles theorem angles are
( overline{ad} )	congruent.

Explanation:

Step1: Recall the property of congruent angles

If two angles are congruent, then their measures are equal. This is a fundamental property in geometry.

Step2: Apply the property to the given angles

Since \( \angle BCA\cong\angle CAD\), by the property "Congruent angles have equal measures", we can say \( m\angle BCA = m\angle CAD\).

Answer:

Congruent angles have equal measures.