Question

Part d move the vertices of the parallelogram around and notice how the measurements from parts b and c change. What conjecture can you make about the sides and the angles of parallelograms?

Answer 1

A conjecture about parallelograms is that their opposite sides are always equal in length, and opposite angles are equal in measure, regardless of how the vertices are moved.

Step-by-step explanation:

The student's question is asked to make a conjecture about the properties of parallelograms based on the observation of changing measurements when the vertices are moved. When working with parallelograms, two key properties are always observed:

• Opposite sides of a parallelogram are equal in length.
• Opposite angles of a parallelogram are equal in measure.

Therefore, no matter how the vertices of the parallelogram are rearranged, as long as the shape remains a parallelogram, these properties will hold true. The adjacent angles are supplementary, and the diagonals of parallelograms bisect each other. Also, each diagonal of a parallelogram divides it into two congruent triangles.