Exercises: Classifying Two-Dimensional Figures in a Hierarchy Based on Properties
Work through each section in order. Base every classification on measured properties -- sides, angles, and parallel sides -- not on how a shape looks or is oriented.
Recall / Warm-Up
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?
At least one pair of parallel sides
Exactly one pair of parallel sides
Four equal sides
Four right angles
A rectangle has four right angles and opposite sides equal. Does a rectangle have at least one pair of parallel sides?
Yes -- a rectangle is a parallelogram, which has two pairs of parallel sides, so it certainly has at least one.
No -- rectangles are defined only by their right angles, not by 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: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Fluency Practice
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?
Always true
Sometimes true -- only when the trapezoid also has a second pair of parallel sides
Never true
Cannot be determined
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?
Four right angles
Four equal sides
Two pairs of parallel sides
None of these properties
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)?
Equilateral acute
Isosceles right
Scalene obtuse
Equilateral right
Is an equilateral triangle also an isosceles triangle?
Yes -- isosceles means at least two equal sides, and three equal sides certainly satisfies that.
No -- isosceles means exactly two equal sides, and an equilateral triangle has three.
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?
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