Classify 2D Shapes

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Answer Key & Explanations

Classify 2D Shapes · Grade 4 · Worksheet 2

1. Hana draws a quadrilateral with exactly one pair of parallel sides and no perpendicular sides. What is the name of this shape? Answer: trapezoid Solution: Recall the properties of quadrilaterals. A quadrilateral is a 4-sided shape. The shape has exactly one pair of parallel sides.
   Full step-by-step solution

   Step 1: Recall the properties of quadrilaterals. A quadrilateral is a 4-sided shape. Step 2: The shape has exactly one pair of parallel sides. This means two sides are parallel, and the other two are not. Step 3: A trapezoid (or trapezium in some countries) is defined as a quadrilateral with at least one pair of parallel sides. Since it says exactly one pair, it is a trapezoid. Step 4: The shape has no perpendicular sides, which is fine for a trapezoid. Not all trapezoids have right angles. The answer is trapezoid.

2. A quadrilateral has two pairs of parallel sides, all sides are equal in length, and its diagonals are perpendicular. What is the name of this shape? Answer: rhombus Solution: List the properties given: two pairs of parallel sides (so it is a parallelogram), all sides equal in length, and diagonals are perpendicular. A parallelogram with all sides equal is either a rhombus or a square. A square has all angles 90 degrees, but the problem does not mention right angles.
   Full step-by-step solution

   Step 1: List the properties given: two pairs of parallel sides (so it is a parallelogram), all sides equal in length, and diagonals are perpendicular. Step 2: A parallelogram with all sides equal is either a rhombus or a square. Step 3: A square has all angles 90 degrees, but the problem does not mention right angles. It only says diagonals are perpendicular. Step 4: A rhombus has all sides equal, opposite sides parallel, and its diagonals are perpendicular (but not necessarily equal). This matches all given properties. The answer is rhombus.

3. Aroha draws a quadrilateral with exactly one pair of parallel sides and no perpendicular sides. Which type of quadrilateral did Aroha draw? Answer: trapezoid Solution: Recall the types of quadrilaterals: square, rectangle, rhombus, parallelogram, trapezoid. A square has two pairs of parallel sides and perpendicular sides.
   Full step-by-step solution

   Step 1: Recall the types of quadrilaterals: square, rectangle, rhombus, parallelogram, trapezoid. Step 2: A square has two pairs of parallel sides and perpendicular sides. Step 3: A rectangle has two pairs of parallel sides and perpendicular sides. Step 4: A rhombus has two pairs of parallel sides and no perpendicular sides. Step 5: A parallelogram has two pairs of parallel sides and may or may not have perpendicular sides. Step 6: A trapezoid has exactly one pair of parallel sides. Step 7: The shape has exactly one pair of parallel sides and no perpendicular sides, so it must be a trapezoid. The answer is trapezoid.

4. Hana draws a quadrilateral with 4 sides. All sides are equal in length, and opposite sides are parallel. The shape has no right angles. What is the name of this shape? Answer: rhombus Solution: The shape has 4 sides, so it is a quadrilateral. Step 2: All sides are equal in length. Step 3: Opposite sides are parallel.
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: All sides are equal in length. Step 3: Opposite sides are parallel. Step 4: There are no right angles. A square has equal sides and parallel sides, but it has right angles. A rhombus has equal sides, parallel opposite sides, and does not have right angles. Therefore, the shape is a rhombus. The answer is rhombus.

5. A regular octagon has how many lines of symmetry? Answer: 8 Solution: A regular octagon has 8 equal sides and 8 equal angles. Lines of symmetry can go through opposite vertices (corner to corner). For an octagon, there are 4 such lines.
   Full step-by-step solution

   Step 1: A regular octagon has 8 equal sides and 8 equal angles. Step 2: Lines of symmetry can go through opposite vertices (corner to corner). For an octagon, there are 4 such lines. Step 3: Lines of symmetry can also go through the midpoints of opposite sides. For an octagon, there are 4 such lines. Step 4: Total lines of symmetry = 4 + 4 = 8. The answer is 8.

6. Noah is drawing a large decorative star for a school project. The star is made by overlapping two identical squares, each with sides of 12 inches. The squares are rotated so that one square is turned 45 degrees and placed exactly on top of the other, with their centers aligned. How many lines of symmetry does this star shape have? Answer: 4 Solution: Consider a single square. It has 4 lines of symmetry: two through the midpoints of opposite sides, and two through opposite vertices.
   Full step-by-step solution

   Step 1: Consider a single square. It has 4 lines of symmetry: two through the midpoints of opposite sides, and two through opposite vertices. Step 2: When we overlap two identical squares rotated 45 degrees relative to each other, their centers are aligned. The resulting star shape is an 8-pointed star. Step 3: This star has 4 lines of symmetry: one vertical line, one horizontal line, and two diagonal lines at 45 degrees. Each line passes through opposite points of the star. Step 4: You can verify by imagining folding along these lines - both halves would match exactly. The answer is 4.

7. A quadrilateral has two pairs of parallel sides and all sides are equal in length. Does it have perpendicular diagonals? Answer: Yes Solution: Identify the shape. A quadrilateral with two pairs of parallel sides and all sides equal is a rhombus (a square is a special rhombus). Step 2: Recall the property of a rhombus: its diagonals are perpendicular bisectors of each other.
   Full step-by-step solution

   Step 1: Identify the shape. A quadrilateral with two pairs of parallel sides and all sides equal is a rhombus (a square is a special rhombus). Step 2: Recall the property of a rhombus: its diagonals are perpendicular bisectors of each other. Step 3: Therefore, the diagonals are perpendicular. The answer is Yes.