Classify the quadrilateral. Parallel sides are indicated with arrows.
trapezoid
• parallelogram
• rhombus
• rectangle
To classify a quadrilateral based on the presence of parallel sides and indication with arrows, follow these steps:
1. Check if the quadrilateral has exactly one pair of parallel sides. This is indicated by the arrows. If the quadrilateral has more than one pair of parallel sides, it cannot be classified as a trapezoid.
2. If the quadrilateral has exactly one pair of parallel sides, check if the other pair of opposite sides are also parallel. If the opposite sides are parallel, then the quadrilateral can be classified as a parallelogram.
3. If the quadrilateral has exactly one pair of parallel sides and all sides are equal in length, it can be classified as a rhombus. Note that a rhombus is a type of parallelogram, so it will also meet the conditions for a parallelogram classification.
4. If the quadrilateral has exactly one pair of parallel sides, all sides are equal in length, and all angles are right angles, it can be classified as a rectangle. Note that a rectangle is a type of parallelogram and a type of rhombus, so it will also meet the conditions for both a parallelogram and a rhombus classification.
Therefore, based on the given information, the quadrilateral can be classified as:
- a trapezoid if it has exactly one pair of parallel sides.
- a parallelogram if it has exactly one pair of parallel sides and the other pair of opposite sides are also parallel.
- a rhombus if it has exactly one pair of parallel sides, all sides are equal in length, and all angles are right angles.
- a rectangle if it has exactly one pair of parallel sides, all sides are equal in length, all angles are right angles, and the parallel sides are indicated with arrows.