Classify 2D Shapes

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Answer Key & Explanations

Classify 2D Shapes · Grade 4 · Worksheet 3

1. Matiu draws a quadrilateral with exactly one pair of parallel sides and no perpendicular sides. What is the name of this shape? Answer: trapezoid Solution: Identify the shape as a quadrilateral (4-sided polygon). The shape has exactly one pair of parallel sides. This rules out parallelograms, rectangles, squares, and rhombuses, which all have two pairs of parallel sides.
   Full step-by-step solution

   Step 1: Identify the shape as a quadrilateral (4-sided polygon). Step 2: The shape has exactly one pair of parallel sides. This rules out parallelograms, rectangles, squares, and rhombuses, which all have two pairs of parallel sides. Step 3: The shape has no perpendicular sides, so it cannot be a right trapezoid or any shape with right angles. Step 4: A quadrilateral with exactly one pair of parallel sides is called a trapezoid (or trapezium in some countries). The answer is trapezoid.

2. A quadrilateral has 4 sides. It has exactly 1 pair of parallel sides and 0 perpendicular sides. What is the name of this shape? Answer: trapezoid Solution: The shape is a quadrilateral, meaning it has 4 sides. Step 2: It has exactly 1 pair of parallel sides. A shape with exactly one pair of parallel sides is called a trapezoid.
   Full step-by-step solution

   Step 1: The shape is a quadrilateral, meaning it has 4 sides. Step 2: It has exactly 1 pair of parallel sides. A shape with exactly one pair of parallel sides is called a trapezoid. Step 3: The fact that it has 0 perpendicular sides does not change the name; it just means no sides meet at right angles. Step 4: Therefore, the shape is a trapezoid. The answer is trapezoid.

3. Is a regular octagon symmetrical? Answer: Yes Solution: A regular octagon has 8 equal sides and 8 equal angles. It has 8 lines of symmetry: 4 lines through opposite vertices and 4 lines through the midpoints of opposite sides.
   Full step-by-step solution

   A regular octagon has 8 equal sides and 8 equal angles. It has 8 lines of symmetry: 4 lines through opposite vertices and 4 lines through the midpoints of opposite sides. Since you can fold it along any of these lines and both halves match exactly, a regular octagon is symmetrical. The answer is Yes.

4. Isabella is drawing a rectangular garden for her science project. She measures the opposite sides and finds that the top side is 17 inches and the bottom side is also 17 inches. The left side is 12 inches and the right side is also 12 inches. Isabella notices that the two long sides are parallel to each other, and the two short sides are also parallel to each other. When she draws the diagonal lines from opposite corners, they cross each other at a 90-degree angle. Which property of her rectangle does the diagonal crossing at a 90-degree angle describe? Answer: perpendicular lines Solution: Understand what the problem is describing. Isabella draws diagonal lines from opposite corners of the rectangle. Step 2: The problem tells us that these diagonal lines cross at a 90-degree angle.
   Full step-by-step solution

   Step 1: Understand what the problem is describing. Isabella draws diagonal lines from opposite corners of the rectangle. These diagonals cross each other at the center of the rectangle. Step 2: The problem tells us that these diagonal lines cross at a 90-degree angle. Step 3: When two lines meet or cross at a 90-degree angle, they are called perpendicular lines. Step 4: So the property being described is that the diagonals are perpendicular to each other. The answer is perpendicular lines.

5. Emma draws a shape with 4 sides. Two pairs of opposite sides are parallel, and all angles are right angles. Does this shape have any perpendicular sides? Answer: Yes Solution: The shape has 4 sides with two pairs of parallel opposite sides and all right angles. This describes a rectangle. Perpendicular sides meet at a right angle (90 degrees).
   Full step-by-step solution

   Step 1: The shape has 4 sides with two pairs of parallel opposite sides and all right angles. This describes a rectangle. Step 2: Perpendicular sides meet at a right angle (90 degrees). Step 3: Since all angles in the shape are right angles, every pair of adjacent sides are perpendicular. Step 4: Therefore, the shape does have perpendicular sides. The answer is Yes.

6. Mason draws a shape with 8 sides. All sides are equal in length, and all interior angles are equal. Does this shape have perpendicular sides? Answer: No Solution: The shape is a regular octagon (8 equal sides, 8 equal angles). The interior angle of a regular octagon is 135 degrees, not 90 degrees. Perpendicular sides meet at exactly 90 degrees.
   Full step-by-step solution

   Step 1: The shape is a regular octagon (8 equal sides, 8 equal angles). Step 2: The interior angle of a regular octagon is 135 degrees, not 90 degrees. Step 3: Perpendicular sides meet at exactly 90 degrees. Step 4: Since 135 degrees is not 90 degrees, the sides are not perpendicular. The answer is No.

7. Isabella is designing a new quilt pattern. She draws a shape with 4 sides. Two of the sides are parallel to each other, and the other two sides are also parallel to each other. The shape has no perpendicular sides and no lines of symmetry. Which shape did Isabella draw? Answer: D. Parallelogram Solution: The shape has 4 sides, so it is a quadrilateral. Two pairs of sides are parallel. This means it is a parallelogram, rectangle, or square.
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: Two pairs of sides are parallel. This means it is a parallelogram, rectangle, or square. Step 3: It has no perpendicular sides. Perpendicular means sides that meet at a right angle (90 degrees). Rectangles and squares have perpendicular sides, so they are eliminated. Step 4: It has no lines of symmetry. A parallelogram does not have lines of symmetry, while a rectangle and a square do. Step 5: The shape that fits all the clues is a parallelogram. The correct answer is Parallelogram.

8. A regular pentagon has how many lines of symmetry? Answer: 5 Solution: A regular pentagon has 5 equal sides and 5 equal angles. Step 2: Each line of symmetry goes from a vertex to the midpoint of the opposite side. Step 3: Since there are 5 vertices, there are 5 such lines.
   Full step-by-step solution

   Step 1: A regular pentagon has 5 equal sides and 5 equal angles. Step 2: Each line of symmetry goes from a vertex to the midpoint of the opposite side. Step 3: Since there are 5 vertices, there are 5 such lines. Step 4: Therefore, a regular pentagon has 5 lines of symmetry. The answer is 5.