Classifying 2D Shapes — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A square is not a rectangle because all four sides are equal.
Corrected: A square is a rectangle because it has four right angles and two pairs of parallel sides.
The corrected sentence is: "A square is a rectangle because it has four right angles and two pairs of parallel sides.". The original sentence "A square is not a rectangle because all four sides are equal." contained an error that needed to be fixed.
2. Fix the sentence:
A trapezoid has two pairs of parallel sides.
Corrected: A trapezoid has exactly one pair of parallel sides.
The corrected sentence is: "A trapezoid has exactly one pair of parallel sides.". The original sentence "A trapezoid has two pairs of parallel sides." contained an error that needed to be fixed.
3. Fix the sentence:
A rhombus never has right angles.
Corrected: A rhombus can have right angles; when it does, it is also a square.
The corrected sentence is: "A rhombus can have right angles; when it does, it is also a square.". The original sentence "A rhombus never has right angles." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Every square is also a rectangle because it has four right angles.
A rectangle is defined as a quadrilateral with four right angles. Since a square has four right angles and two pairs of equal opposite sides, it meets the definition of a rectangle.
2. A parallelogram has 2 pairs of parallel sides.
A parallelogram has two pairs of parallel and equal opposite sides. This is its defining characteristic.
3. The sum of all interior angles in any quadrilateral is 360 degrees.
Any quadrilateral can be divided into two triangles, each with angles summing to 180°. So 180° × 2 = 360° for the quadrilateral.
4. A quadrilateral with exactly one pair of parallel sides is called a trapezoid.
A trapezoid has exactly one pair of parallel sides (called bases). Unlike a parallelogram, the other pair of sides is not parallel.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why every rectangle is a parallelogram but not every parallelogram is a rectangle.
Sample answer: Every rectangle has two pairs of parallel sides, so it is a parallelogram. However, a parallelogram does not need right angles, so not every parallelogram is a rectangle.
Rectangle ⊂ Parallelogram: rectangles have all parallelogram properties plus four right angles. But parallelograms can have non-right angles (like a slanted rhombus), so they are not always rectangles.
2. Is every rhombus a square? Explain your reasoning.
Sample answer: No. A rhombus has four equal sides, but it does not always have four right angles. Only when a rhombus has four right angles is it also a square.
A square is a special rhombus — it has all four equal sides (rhombus) plus four right angles (rectangle). A rhombus without right angles is not a square.