This sheet pushes the quadrilateral hierarchy as far as fifth grade goes. You spot the false diagonal claim about parallelograms, identify a four-equal-sided shape with no right angles as a rhombus, and count the five categories a square belongs to — square, rhombus, rectangle, parallelogram, quadrilateral.
Fill-in items reach further: a 1440° angle sum gives a 10-sided polygon, a 40° exterior angle gives nine sides, and a shape that is both rectangle and rhombus must be a square. The diagonal formula n × (n − 3) ÷ 2 ties it together. This is the reasoning bridge from naming shapes to proving why they belong where they do.
Style:
Classifying 2D Shapes
Part A: Multiple Choice
Circle the best answer for each question.
1. Which statement about diagonals is FALSE?
A) A square's diagonals are equal and perpendicular
B) A rectangle's diagonals are equal but not perpendicular
C) A rhombus's diagonals are perpendicular but not always equal
D) A parallelogram's diagonals are always equal
2. A quadrilateral has two pairs of parallel sides, four equal sides, and no right angles. What is it?
A) Square
B) Rectangle
C) Rhombus
D) Trapezoid
3. How many categories does a square belong to: square, rhombus, rectangle, parallelogram, quadrilateral?
A) 2
B) 3
C) 4
D) 5
4. A regular polygon has an interior angle sum of 1440°. How many sides does it have?
A) 8
B) 9
C) 10
D) 12
Part B: Fill in the Blank
Write the correct answer on each line.
1. Every rectangle is a parallelogram, but not every parallelogram is a rectangle because parallelograms do not require right angles.
2. The diagonals of a kite cross at right angles, and exactly 1 of the diagonals is bisected by the other.
3. If a regular polygon has an exterior angle of 40°, it has 9 sides.
4. A shape that is both a rectangle and a rhombus must be a square.
5. The number of diagonals in any polygon with n sides is n × (n − 3) ÷ 2.
Classifying 2D Shapes
★ Part A: Multiple Choice
Circle the best answer for each question.
1. Which statement about diagonals is FALSE?
A) A square's diagonals are equal and perpendicular
B) A rectangle's diagonals are equal but not perpendicular
C) A rhombus's diagonals are perpendicular but not always equal
D) A parallelogram's diagonals are always equal
2. A quadrilateral has two pairs of parallel sides, four equal sides, and no right angles. What is it?
A) Square
B) Rectangle
C) Rhombus
D) Trapezoid
3. How many categories does a square belong to: square, rhombus, rectangle, parallelogram, quadrilateral?
A) 2
B) 3
C) 4
D) 5
4. A regular polygon has an interior angle sum of 1440°. How many sides does it have?
A) 8
B) 9
C) 10
D) 12
★ Part B: Fill in the Blank
Write the correct answer on each line.
1) Every rectangle is a parallelogram, but not every parallelogram is a rectangle because parallelograms do not require right angles.
2) The diagonals of a kite cross at right angles, and exactly 1 of the diagonals is bisected by the other.
3) If a regular polygon has an exterior angle of 40°, it has 9 sides.
4) A shape that is both a rectangle and a rhombus must be a square.
5) The number of diagonals in any polygon with n sides is n × (n − 3) ÷ 2.
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