Exercises: Classifying Two-Dimensional Figures in a Hierarchy Based on Properties

This lesson uses the definition of trapezoid as a quadrilateral with AT LEAST one pair of parallel sides. Under this definition, which property is required for a shape to be classified as a trapezoid?

A rectangle has four right angles and opposite sides equal. Does a rectangle have at least one pair of parallel sides?

A square has four equal sides and four right angles. Besides square, rectangle, and rhombus, name the category directly above rectangle and rhombus in the hierarchy that a square also belongs to:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

In the quadrilateral tree, quadrilateral branches to trapezoid (at least one pair of parallel sides). Trapezoid branches to parallelogram (  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   pairs of parallel sides). Parallelogram branches to rectangle (parallelogram, plus four   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ).

Consider the statement: "A trapezoid is a parallelogram." Is this statement always true, sometimes true, or never true?

A square has four right angles, four equal sides, and two pairs of parallel sides. Which of these properties is the one that specifically makes it a member of the rectangle category?

A triangle has sides of length 5, 5, and 5, and all three angles measure 60 degrees. What is its complete classification (side type and angle type)?

Is an equilateral triangle also an isosceles triangle?

A shape has four right angles and opposite sides equal in length, but its sides are not all the same length. Counting quadrilateral, trapezoid, parallelogram, and rectangle, how many of these four category names correctly describe this shape?