Question

practice & problem solving
understand

1. use appropriate tools if you are given

a drawing of a quadrilateral, how can
you determine whether or not it is a
parallelogram? what tool or tools can you use?

Explanation:

A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel and equal in length, or with opposite angles equal, or with diagonals that bisect each other. To verify this from a drawing, use tools to measure side lengths, angles, or diagonal segments:

1. A ruler can measure side lengths to check if opposite sides are equal, or measure the segments of bisected diagonals.
2. A protractor can measure interior angles to confirm opposite angles are equal, or check if consecutive angles are supplementary (sum to $180^\circ$).
3. A straightedge can be used to extend sides and visually check if opposite sides are parallel, or a set square can help confirm parallelism by aligning right angles with the sides.

Answer:

To determine if the quadrilateral is a parallelogram, verify one of its defining properties:

1. Check if both pairs of opposite sides are equal in length (use a ruler to measure all four sides and compare opposite pairs).
2. Check if both pairs of opposite angles are equal (use a protractor to measure all four interior angles and compare opposite pairs).
3. Check if the diagonals bisect each other (draw the diagonals, use a ruler to measure the segments of each diagonal from their intersection point to the vertices; the two segments of each diagonal should be equal).
4. Check if both pairs of opposite sides are parallel (use a straightedge/set square to confirm opposite sides never intersect when extended, or use a protractor to check consecutive angles are supplementary, summing to $180^\circ$).

Tools to use: Ruler, protractor, straightedge, or set square.