Classifying 2D Shapes — Answer Key
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
A parallelogram's diagonals bisect each other but are NOT always equal in length — only rectangles and squares (special parallelograms) guarantee equal diagonals.
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
Two pairs of parallel sides with four equal sides describes a rhombus; the detail "no right angles" rules out a square, which is a special rhombus that does have right angles.
3. How many categories does a square belong to: square, rhombus, rectangle, parallelogram, quadrilateral?
A) 2
B) 3
C) 4
D) 5
A square fits all five categories because it has four equal sides (rhombus), four right angles (rectangle), two pairs of parallel sides (parallelogram), and four sides (quadrilateral).
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
Using the formula (n - 2) x 180° = 1440°, solve for n: n - 2 = 8, so n = 10 sides, making it a regular decagon.
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.
A rectangle requires all four angles to be 90°, but a general parallelogram only needs opposite sides parallel — so without right angles, a parallelogram is not a rectangle.
2. The diagonals of a kite cross at right angles, and exactly 1 of the diagonals is bisected by the other.
In a kite, the longer diagonal (the axis of symmetry) bisects the shorter one at right angles, but the shorter diagonal does not bisect the longer one — so only 1 diagonal is bisected.
3. If a regular polygon has an exterior angle of 40°, it has 9 sides.
Exterior angles of any convex polygon sum to 360°, so dividing 360° by the 40° exterior angle gives 360° / 40° = 9 sides.
4. A shape that is both a rectangle and a rhombus must be a square.
A rectangle has four right angles and a rhombus has four equal sides, so a shape with both properties — four equal sides and four right angles — must be a square.
5. The number of diagonals in any polygon with n sides is n × (n − 3) ÷ 2.
You divide by 2 because each diagonal connects two vertices, and without dividing you would count every diagonal twice — once from each end.