Classify 2D Shapes

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Answer Key & Explanations

Classify 2D Shapes · Grade 4 · Worksheet 3

1. Aroha draws a quadrilateral with exactly one pair of parallel sides and no perpendicular sides. What is the name of this shape? Answer: trapezoid Solution: A quadrilateral is a shape with 4 sides. Step 2: The shape has exactly one pair of parallel sides.
   Full step-by-step solution

   Step 1: A quadrilateral is a shape with 4 sides. Step 2: The shape has exactly one pair of parallel sides. Step 3: A trapezoid (or trapezium in some countries) is defined as a quadrilateral with exactly one pair of parallel sides. Step 4: The shape has no perpendicular sides, which is fine for a trapezoid. Step 5: Therefore, the shape is a trapezoid.

2. Charlotte is designing a large rectangular garden for her school's outdoor classroom. She draws a rectangle that is 25 feet long and 14 feet wide. She then draws a line of symmetry from the top edge to the bottom edge through the center. Next, she wonders: if she draws a diagonal line from one corner to the opposite corner, will that diagonal also be a line of symmetry for the rectangle? Explain your answer by describing the properties of the rectangle and how lines of symmetry work. Answer: No, a diagonal line is not a line of symmetry for a rectangle that is not a square. A rectangle has exactly two lines of symmetry: one vertical through the middle and one horizontal through the middle. A diagonal does not create two identical mirror-image halves because the two sides of the rectangle are different lengths (25 ft and 14 ft). Solution: Recall the definition of a line of symmetry. A line of symmetry divides a shape into two identical mirror-image halves. Charlotte's rectangle has a length of 25 feet and a width of 14 feet.
   Full step-by-step solution

   Step 1: Recall the definition of a line of symmetry. A line of symmetry divides a shape into two identical mirror-image halves. When you fold along the line, one side exactly matches the other. Step 2: Charlotte's rectangle has a length of 25 feet and a width of 14 feet. Opposite sides are parallel and equal, and all four angles are right angles. Step 3: Consider a vertical line through the center from top to bottom. The left half is 12.5 feet wide and 14 feet tall, and the right half is also 12.5 feet wide and 14 feet tall. These are mirror images, so this is a line of symmetry. Step 4: Consider a horizontal line through the center from left to right. The top half is 25 feet wide and 7 feet tall, and the bottom half is also 25 feet wide and 7 feet tall. These are mirror images, so this is a second line of symmetry. Step 5: Now consider a diagonal line from the top-left corner to the bottom-right corner. When you fold along this line, the top-right part of the rectangle does not match the bottom-left part. The top-right part has a width of 14 feet and a height of 25 feet, but the bottom-left part has a width of 25 feet and a height of 14 feet. These are not identical because the sides are different lengths. Step 6: A diagonal line only becomes a line of symmetry if the rectangle is a square (all sides equal). Since 25 ft is not equal to 14 ft, the diagonal is not a line of symmetry. The answer is: No, a diagonal line is not a line of symmetry for this rectangle.

3. Matiu is designing a large garden plot for his community. He draws a quadrilateral that has two pairs of parallel sides and four right angles. All four sides are not the same length. Matiu wants to add a line of symmetry to his design. How many lines of symmetry does Matiu's shape have? Answer: 2 Solution: Identify the shape. Matiu's shape has two pairs of parallel sides and four right angles, but not all sides are equal. This describes a rectangle.
   Full step-by-step solution

   Step 1: Identify the shape. Matiu's shape has two pairs of parallel sides and four right angles, but not all sides are equal. This describes a rectangle. Step 2: Consider lines of symmetry for a rectangle. A line of symmetry divides a shape into two identical mirror-image halves. Step 3: A rectangle has a vertical line of symmetry through the middle (left side matches right side). Step 4: A rectangle also has a horizontal line of symmetry through the middle (top side matches bottom side). Step 5: Diagonal lines do not work because the sides are not equal, so the two halves would not match. Step 6: Therefore, a rectangle has exactly 2 lines of symmetry. The answer is 2.

4. Emma is designing a large mosaic for her school's art show. She draws a quadrilateral with 4 sides of equal length. The shape has two pairs of parallel sides, but none of its angles are right angles. Emma then draws a line through the shape that connects two opposite corners. She notices that this line creates two identical mirror-image triangles. Does Emma's shape have exactly 1 line of symmetry, more than 1 line of symmetry, or no lines of symmetry? Answer: More than 1 line of symmetry (a rhombus has 2 lines of symmetry) Solution: Identify the shape. A quadrilateral with all sides equal, opposite sides parallel, and no right angles is a rhombus. Step 2: Recall the lines of symmetry of a rhombus.
   Full step-by-step solution

   Step 1: Identify the shape. A quadrilateral with all sides equal, opposite sides parallel, and no right angles is a rhombus. Step 2: Recall the lines of symmetry of a rhombus. A rhombus has exactly 2 lines of symmetry: one through each pair of opposite vertices (diagonal folds). Step 3: The problem states that one diagonal line creates two identical mirror-image triangles, confirming that is a line of symmetry. Step 4: The other diagonal also creates two identical mirror-image triangles, giving a second line of symmetry. Step 5: Folding through the midpoints of opposite sides does not work because the sides are not perpendicular, so there are no horizontal or vertical lines of symmetry. Step 6: Since the rhombus has 2 lines of symmetry, that is more than 1 line of symmetry. The answer is: More than 1 line of symmetry.

5. Sophia is drawing a large rectangular garden in her notebook. She draws a shape that has exactly 4 sides and 4 right angles. All four sides are not the same length, but opposite sides are parallel. Which two-dimensional shape has Sophia drawn? Answer: rectangle Solution: The shape has 4 sides and 4 right angles. A quadrilateral with 4 right angles is either a square or a rectangle. Step 2: The problem says all four sides are not the same length.
   Full step-by-step solution

   Step 1: The shape has 4 sides and 4 right angles. A quadrilateral with 4 right angles is either a square or a rectangle. Step 2: The problem says all four sides are not the same length. A square has all sides equal, so it cannot be a square. Step 3: Opposite sides are parallel, which is true for a rectangle. Therefore, the shape Sophia drew is a rectangle.