Classifying Quadrilaterals — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Shapes A-H include square, rectangle, rhombus, parallelogram, trapezoid, kite, and two general quadrilaterals. Which Grade 4 group must include the square AND the rhombus?
A) Rectangles
B) Parallelograms
C) Trapezoids
D) Kites only
Both squares and rhombuses have two pairs of parallel sides, so both are parallelograms in the Grade 4 hierarchy.
2. Out of 8 shapes, only the square belongs to all four groups: parallelogram, rectangle, rhombus, and square. Why?
A) It has only one pair of parallel sides
B) It has 4 equal sides AND 4 right angles
C) It has only equal diagonals
D) It has no lines of symmetry
A square has 4 congruent sides (rhombus attribute) and 4 right angles (rectangle attribute), so it fits every group above.
3. Which Grade 4 shape from the set fits ONLY the trapezoid category and no other parallelogram category?
A) Square
B) Rhombus
C) Isosceles trapezoid
D) Rectangle
An isosceles trapezoid has only one pair of parallel sides, so it is a trapezoid but not a parallelogram, rectangle, or rhombus.
4. If a shape is a rectangle but NOT a square, which Grade 4 categories does it belong to?
A) Rhombus and square
B) Parallelogram and rectangle
C) Trapezoid only
D) Kite and rhombus
Every rectangle is a parallelogram. Without 4 equal sides it is not a rhombus or square, so it stays in parallelogram and rectangle groups.
Part B: Fill in the Blank
Write the correct answer on each line.
1. In the Grade 4 quadrilateral hierarchy, every square is also a rhombus.
A square has 4 congruent sides, so it satisfies the rhombus definition; every square is a rhombus.
2. A shape with 4 equal sides and 4 right angles fits in 4 Grade 4 categories at once.
A square fits parallelogram, rectangle, rhombus, and square - 4 categories - because it shares attributes with each.
3. An isosceles trapezoid is sorted into the trapezoid category only.
An isosceles trapezoid has one pair of parallel sides, so it belongs only to the trapezoid group, not parallelograms.
4. A non-square rhombus sorts into rhombus and parallelogram categories.
Every rhombus is a parallelogram; if it lacks right angles it is not a rectangle or square.
5. A general (scalene) parallelogram fits only the parallelogram category among the four families.
Without congruent sides or right angles, it cannot be a rhombus, rectangle, or square - only a parallelogram.