Math / Geometry

QuestionChoose ALL answers that describe the polygon $D E F G$ if $D E=E F=F G=G D$ .
Answer Attempt 2 out of 3 Parallelogram Quadrilateral Rectangle Rhombus Square Trapezoid Submit Answer

Studdy Solution

STEP 1

1. The polygon $DEFG$ is a quadrilateral.
2. All sides of the polygon are equal, i.e., $DE = EF = FG = GD$ .

STEP 2

1. Determine the basic classification of the polygon.
2. Analyze specific properties based on equal sides.
3. Evaluate each given option to determine if it fits the properties of the polygon.

STEP 3

Since $DEFG$ has four sides, it is a quadrilateral.

STEP 4

With all sides equal, the polygon is a rhombus. A rhombus is defined as a quadrilateral with all sides of equal length.

STEP 5

Evaluate each option:
- Parallelogram: A rhombus is a type of parallelogram, so this is true. - Quadrilateral: By definition, $DEFG$ is a quadrilateral, so this is true. - Rectangle: A rectangle requires opposite sides to be equal and all angles to be $90^\circ$ . We cannot assume $DEFG$ is a rectangle without additional angle information, so this is false. - Rhombus: As determined, $DEFG$ is a rhombus, so this is true. - Square: A square is a rhombus with all angles $90^\circ$ . Without angle information, we cannot assume $DEFG$ is a square, so this is false. - Trapezoid: A trapezoid has at least one pair of parallel sides. Without angle or parallel side information, we cannot assume $DEFG$ is a trapezoid, so this is false.
The polygon $DEFG$ can be described as:
- Parallelogram - Quadrilateral - Rhombus

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