Exercises: Property Inheritance in Two-Dimensional Figure Categories
Work through each section in order. For true/false and justification problems, base your answer on definitions and properties -- not on how a shape looks.
Recall / Warm-Up
Which shape has two pairs of parallel sides AND all four sides equal in length?
Parallelogram
Rectangle
Rhombus
Trapezoid
Look at the parallelogram shown. Which pairs of sides are parallel?
Only the top and bottom sides
Only the left and right sides
Both pairs of opposite sides
No sides are parallel
A shape with exactly four sides and four right angles is called a ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Fluency Practice
All parallelograms have opposite angles that are equal. Rhombuses are parallelograms. Therefore, all rhombuses have opposite angles that are ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
All rectangles have four right angles. Squares are rectangles. What can you conclude?
All squares have four right angles.
All squares have four equal sides.
Some squares have right angles.
No conclusion can be drawn.
In the quadrilateral hierarchy diagram, the parallelogram region contains two overlapping regions: rectangles and rhombuses. The region that sits inside BOTH the rectangle region and the rhombus region represents the shape called the ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Which shape belongs to the parallelogram subcategory but does NOT belong to either the rectangle or the rhombus subcategory?
A square
A parallelogram with unequal sides and no right angles
A trapezoid with only one pair of parallel sides
A general quadrilateral with no parallel sides
A quadrilateral has 4 sides. A parallelogram is a quadrilateral with 2 pairs of parallel sides. A rectangle is a parallelogram with 4 right angles. How many of these three category names -- quadrilateral, parallelogram, rectangle -- correctly describe a square?
Every square has opposite sides equal in length. Why is this true?
Because squares are parallelograms, and all parallelograms have opposite sides equal.
Because someone measured every square that exists.
Because squares are a separate category with no relation to parallelograms.
This is not actually true for squares.
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