Question

Polygons with four sides are called quadrilaterals. Sort the quadrilaterals in the shapes into two or more subgroups. What properties do the subgroup members share?

a) Parallel sides
b) Equal angles
c) Opposite sides equal
d) All of the above

Answer 1

Quadrilaterals can be categorized as parallelograms, rectangles, squares, and rhombuses based on properties like parallel sides, equal angles, and opposite sides being equal. Each subgroup has distinct characteristics that help in classification.

Step-by-step explanation:

Quadrilaterals can be sorted into different subgroups based on certain properties they share. These properties include:

• Parallel sides: Quadrilaterals with both pairs of opposite sides parallel are called parallelograms.
• Equal angles: A rectangle is an example of a quadrilateral with four right angles.
• Opposite sides equal: Rectangles and parallelograms both have equal opposite sides.
• All of the above: A square has all the properties mentioned above; it has parallel sides, four equal angles, and equal opposite sides.

To sort quadrilaterals into subgroups based on the above properties, we could have:

• Parallelograms (having both parallel sides and opposite sides equal)
• Rectangles (having equal angles, opposite sides equal, and also parallel sides)
• Squares (having all the properties: parallel sides, equal angles, and opposite sides equal)
• Rhombuses (having all sides equal, opposite sides parallel)

Each subgroup has unique characteristics that define the relationships between their sides and angles. Knowing these properties helps in the mathematical description and categorization of different quadrilaterals.