Are these quadrilaterals parallelograms?

(quadrilateral ABCD with diagonals intersecting at E)

1. AB is congruent to AD and AB is parallel to DC
2. AB and DC are congruent and parallel
3. DE and BE are congruent

A parallelogram is a quadrilateral with

its opposite sides parallel and equal.
The opposite angles are also equal.

1. Yes.
2. Yes.
3. Yes.

To determine whether quadrilaterals are parallelograms, we need to check if certain properties are satisfied.

1. To check if quadrilateral ABCD with diagonals intersecting at E is a parallelogram, we need to verify if AB is congruent to AD and if AB is parallel to DC.
- To check congruence, measure line segment AB and compare it to the length of line segment AD. If they are equal, then AB is congruent to AD.
- To check if AB is parallel to DC, compare the slopes of AB and DC. If the slopes are equal, then AB is parallel to DC. If both conditions are met, then the quadrilateral is a parallelogram.

2. To determine if AB and DC are congruent and parallel, we need to check if both conditions are satisfied.
- Check for congruence by measuring the length of line segment AB and line segment DC. If they are equal in length, then AB and DC are congruent.
- To check for parallel lines, compare the slopes of line segment AB and line segment DC. If the slopes are equal, then AB is parallel to DC. If both conditions hold true, then the quadrilateral is a parallelogram.

3. To check if DE and BE are congruent, measure the length of line segment DE and compare it to the length of line segment BE. If they are equal, then DE and BE are congruent. However, this information alone does not determine whether the quadrilateral is a parallelogram.

In summary, to determine if a quadrilateral is a parallelogram, you need to check for congruent sides and parallel sides. Each condition should be satisfied to conclude that the quadrilateral is a parallelogram.