Standard: 5.G.B.3
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories
of that category. For example, all rectangles have four right angles and squares are rectangles, so all
squares have four right angles.
Math Practice Standards: MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7
Task Exemplars:
1. Write “True” or “False” for each of the statements below. If a statement is false,
rewrite it so that it is true.
a. All rhombuses are parallelograms. Parallelograms have 2 pairs of parallel
sides. Therefore, all rhombuses have 2 pairs of parallel sides.
b. All rectangles have 4 right angles. Squares have 4 right angles. Therefore, all
squares are rectangles.
c. Some quadrilaterals have 4 equal sides. Squares have 4 equal sides. Therefore,
all quadrilaterals are squares.
d. All equilateral triangles have 3 equal sides. Isosceles triangles have at least 2
equal sides. Therefore, all isosceles triangles are equilateral triangles.
e. The opposite sides of parallelograms are equal. Therefore, the opposite sides of
any rectangle are equal.
f. Every property of parallelograms is also a property of all rectangles.
g. Every property of triangles is also a property of quadrilaterals.
2. Describe the properties of a shape that is both a rectangle and a rhombus. Draw an
example.
3. All parallelograms have 4 sides, 4 vertices, and 2 pairs of parallel sides. All
rhombuses have 4 equal sides, 4 vertices, and 2 pairs of parallel sides. Julia says
that all parallelograms are rhombuses, but not all rhombuses are parallelograms.
Is she correct? Why or why not?