Question

1. $overline{ab}paralleloverline{dc};overline{ad}paralleloverline{bc}$
2. $angle1congangle5;angle2congangle6$
3. $angle4congangle5;angle3congangle6$
4. $angle1congangle4;angle2congangle3$ 5. transitive property

what are the missing reasons in this proof that opposite angles of parallelogram abcd are congruent?
definition of a parallelogram
two parallel segments are intersected by a transversal, alternate interior angles are congruent.
two parallel segments are intersected by a transversal, corresponding angles are congruent.
definition of a parallelogram
two parallel segments are intersected by a transversal, corresponding angles are congruent.
two parallel segments are intersected by a transversal, alternate interior angles are congruent.
opposite sides of any quadrilateral are parallel
two parallel segments are intersected by a transversal, corresponding angles are congruent.
two parallel segments are intersected by a transversal, alternate interior angles are congruent.
opposite sides of any quadrilateral are parallel
two parallel segments are intersected by a transversal, alternate interior angles are congruent.
two parallel segments are intersected by a transversal, corresponding angles are congruent.

Explanation:

1. Given $\overline{AB}\parallel\overline{DC}$ and $\overline{AD}\parallel\overline{BC}$, this is the definition of a parallelogram.
2. For $\angle1\cong\angle5$ and $\angle2\cong\angle6$, when two parallel - segments are intersected by a transversal, corresponding angles are congruent.
3. For $\angle4\cong\angle5$ and $\angle3\cong\angle6$, when two parallel - segments are intersected by a transversal, alternate interior angles are congruent.

Answer:

Definition of a parallelogram
Two parallel segments are intersected by a transversal, corresponding angles are congruent
Two parallel segments are intersected by a transversal, alternate interior angles are congruent