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 rectangle has exactly one line of symmetry.
Corrected: A rectangle has exactly two lines of symmetry.
A rectangle can be folded in half both horizontally and vertically to create matching halves, giving it exactly two lines of symmetry, not one.
2. Fix the sentence:
All quadrilaterals have equal diagonals.
Corrected: Only some quadrilaterals, such as rectangles and squares, have equal diagonals.
Most quadrilaterals, like parallelograms and trapezoids, have diagonals of different lengths; only special ones like rectangles and squares have equal diagonals.
3. Fix the sentence:
A pentagon has four lines of symmetry when it is regular.
Corrected: A regular pentagon has five lines of symmetry.
A regular polygon always has as many lines of symmetry as it has sides, so a regular pentagon has five lines of symmetry, not four.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A regular octagon has 8 lines of symmetry.
A regular polygon has the same number of lines of symmetry as sides, so a regular octagon (8 sides) has 8 lines of symmetry.
2. The diagonals of a parallelogram bisect each other.
In every parallelogram, the diagonals cross at their midpoints, meaning each diagonal cuts the other into two equal halves — this is what "bisect" means.
3. A shape with all sides equal but not all angles equal is an irregular polygon.
If all sides are equal but the angles differ, the shape cannot be regular (which requires both equal sides and equal angles), so it is classified as an irregular polygon.
4. A square has 4 lines of symmetry.
A square can be folded along both diagonals and along both midlines (horizontal and vertical), giving it 4 lines of symmetry in total.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why is every square a rhombus but not every rhombus a square?
Sample answer: Every square has four equal sides, which makes it a rhombus. But a rhombus does not need right angles, so a rhombus with non-right angles is not a square.
A good answer includes: Every square has four equal sides, which makes it a rhombus. But a rhombus does not need right angles, so a rhombus with non-right angles is not a square.
2. A shape has six equal sides and six equal angles. Name it and state whether it is regular or irregular.
Sample answer: It is a regular hexagon because all six sides are equal and all six angles are equal.
A good answer includes: It is a regular hexagon because all six sides are equal and all six angles are equal.