Solution: opposite angles are congruent while adjacent angles are supplementary. In addition, we may determine that both pairs of opposite sides are parallel, and once again, we have shown the quadrilateral to be a parallelogram. parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular. The diagonal of a parallelogram separates it into two congruent triangles. The opposite sides of a parallelogram are congruent so we will need two pairs of congruent segments: Parallelograms $ABCD$ and $EFGH$ have four congruent sides but they are not congruent since they have different angles (and also different area). Triangles can be used to prove this rule about the opposite sides. The first is: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Another approach might involve showing that the opposite angles of a quadrilateral are congruent or that the consecutive angles of a quadrilateral are supplementary. ). Also as noted above, students working on this task have multiple opportunities to engage in MP5 ''Use Appropriate Tools Strategically'' as they can use manipulatives or computer software to experiment with constructing different parallelograms. Attribution-NonCommercial-ShareAlike 4.0 International License. First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles. Well, we must show one of the six basic properties of parallelograms to be true! This task would be ideally suited for group work since it is open ended and calls for experimentation. This means we are looking for whether or not both pairs of opposite sides of a quadrilateral are congruent. So what are we waiting for. When we think of parallelograms, we usually think of something like this. In order to see what happens with the parallelograms $ABCD$ and $EFGH$ we focus first on $ABCD$. for (var i=0; i