Classifying 2D Shapes — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which statement is always true?
A) All rectangles are squares
B) All parallelograms are rectangles
C) All squares are parallelograms
D) All trapezoids are parallelograms
All squares have two pairs of parallel and equal opposite sides, which is the definition of a parallelogram. A square is always a parallelogram, but not vice versa.
2. A quadrilateral has four equal sides and angles of 60°, 120°, 60°, and 120°. What shape is it?
A) Square
B) Rectangle
C) Rhombus
D) Trapezoid
Four equal sides → rhombus. The angles are not 90°, so it is not a square. Opposite angles are equal (60°,60°) and (120°,120°) → parallelogram/rhombus.
3. Which shape does NOT always have two pairs of parallel sides?
A) Rectangle
B) Parallelogram
C) Trapezoid
D) Rhombus
A trapezoid has exactly ONE pair of parallel sides. Rectangles, parallelograms, and rhombuses all have two pairs of parallel sides.
4. A parallelogram has one angle of 65°. What are the measures of its other three angles?
A) 65°, 115°, 115°
B) 65°, 65°, 165°
C) 55°, 120°, 120°
D) 65°, 25°, 25°
In a parallelogram, opposite angles are equal and adjacent angles are supplementary. So: opposite = 65°; adjacent = 180−65=115°; opposite of that = 115°. Angles: 65°, 115°, 65°, 115°.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A square belongs to 5 different quadrilateral categories: square, rhombus, rectangle, parallelogram, and quadrilateral.
A square is a member of 5 quadrilateral categories in the hierarchy: quadrilateral → parallelogram → rectangle → rhombus → square. It satisfies all the properties of each.
2. If one angle of a parallelogram is 80°, the adjacent angle measures 100 degrees.
Adjacent angles in a parallelogram are supplementary (sum to 180°). 180 − 80 = 100°.
3. A quadrilateral with one pair of parallel sides and equal non-parallel sides is an isosceles trapezoid.
An isosceles trapezoid has one pair of parallel sides (bases) and two equal non-parallel sides (legs). Its base angles are equal.
4. The diagonals of a square bisect each other at right angles and are equal in length.
A square's diagonals are equal in length (property of rectangles) AND bisect each other at 90° (property of rhombuses). Only the square has both properties.
5. A rectangle has two diagonals that divide it into 4 triangles.
Two diagonals cross each other inside the rectangle, creating 4 triangles. Each diagonal alone divides the rectangle into 2 triangles; both together create 4.