Classify 2D Shapes

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Answer Key & Explanations

Classify 2D Shapes · Grade 4 · Worksheet 1

1. Aroha is drawing a large mosaic pattern for her school's art project. She draws a shape with exactly 4 sides. Two pairs of sides are parallel to each other, and all four sides are the same length. However, none of the corners are square corners (right angles). What is the name of the shape Aroha has drawn? Answer: rhombus Solution: The shape has 4 sides, so it is a quadrilateral. It has two pairs of parallel sides, so it is a parallelogram. All four sides are the same length, so it is a rhombus.
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: It has two pairs of parallel sides, so it is a parallelogram. Step 3: All four sides are the same length, so it is a rhombus. Step 4: It does not have right angles, so it cannot be a square. Therefore, the shape is a rhombus.

2. Noah is designing a large kite for a school project. The main part of the kite is a rhombus shape. He measures the diagonals of the rhombus and finds that they cross each other at a perfect right angle (90 degrees). Does a rhombus always have perpendicular diagonals? Explain your reasoning. Answer: No, a rhombus does not always have perpendicular diagonals. Only a square (a special type of rhombus) always has perpendicular diagonals. A general rhombus may or may not have perpendicular diagonals. Solution: Recall the definition of a rhombus: A quadrilateral with all four sides of equal length. Consider a square. A square has all sides equal AND all angles 90 degrees.
   Full step-by-step solution

   Step 1: Recall the definition of a rhombus: A quadrilateral with all four sides of equal length. Step 2: Consider a square. A square has all sides equal AND all angles 90 degrees. In a square, the diagonals are always perpendicular (they cross at 90 degrees). Step 3: Now consider a rhombus that is NOT a square - for example, a diamond shape that is stretched. In such a rhombus, the diagonals are NOT perpendicular. One diagonal is longer, and they cross at an angle that is not 90 degrees. Step 4: Therefore, the property 'diagonals are perpendicular' is true for squares (a special type of rhombus) but NOT for all rhombuses. The answer is no.

3. Sophia draws a quadrilateral with exactly one pair of parallel sides and no perpendicular sides. What is the name of this shape? Answer: trapezoid Solution: The shape is a quadrilateral, meaning it has 4 sides. It has exactly one 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 one pair of parallel sides. A shape with exactly one pair of parallel sides is called a trapezoid. Step 3: The fact that it has no perpendicular sides does not change the name; it is still a trapezoid. The answer is trapezoid.

4. Mason draws a large quadrilateral on grid paper. The shape has exactly one pair of parallel sides and no sides that are perpendicular. One of the interior angles is greater than 180 degrees. What is the name of this quadrilateral? Answer: trapezoid (or trapezium) Solution: Identify quadrilaterals with one pair of parallel sides. The main one is a trapezoid (also called a trapezium in some countries). Step 2: Check if a trapezoid can have an angle greater than 180 degrees.
   Full step-by-step solution

   Step 1: Identify quadrilaterals with one pair of parallel sides. The main one is a trapezoid (also called a trapezium in some countries). Step 2: Check if a trapezoid can have an angle greater than 180 degrees. Yes, a trapezoid can be concave if one of its interior angles is reflex (greater than 180 degrees). Step 3: Verify that no sides are perpendicular. In a concave trapezoid, the angles are not right angles. The answer is a trapezoid.

5. Ava is examining a large tile on the floor. The tile has exactly 8 sides. Some pairs of opposite sides are parallel to each other, and the tile has 4 lines of symmetry. What is the name of this two-dimensional shape? Answer: regular octagon Solution: Identify the number of sides. The tile has 8 sides, so it is an octagon. Step 2: Consider the symmetry.
   Full step-by-step solution

   Step 1: Identify the number of sides. The tile has 8 sides, so it is an octagon. Step 2: Consider the symmetry. A shape with 8 sides and 4 lines of symmetry is a regular octagon. In a regular octagon, all sides are equal, all angles are equal, and opposite sides are parallel. Step 3: Verify parallel sides. In a regular octagon, each pair of opposite sides are parallel. This matches the description. The answer is a regular octagon.

6. Charlotte is helping her younger brother sort a box of 2D shape tiles. She finds a tile with 4 sides, where exactly one pair of opposite sides is parallel. The tile also has 2 acute angles and 2 obtuse angles. What is the name of this shape? Answer: trapezoid Solution: Identify the shape has 4 sides, so it is a quadrilateral. The shape has exactly one pair of parallel sides. This rules out squares, rectangles, rhombuses, and parallelograms (which have two pairs of parallel sides).
   Full step-by-step solution

   Step 1: Identify the shape has 4 sides, so it is a quadrilateral. Step 2: The shape has exactly one pair of parallel sides. This rules out squares, rectangles, rhombuses, and parallelograms (which have two pairs of parallel sides). Step 3: The shape has 2 acute and 2 obtuse angles, which is common for a trapezoid that is not isosceles. Step 4: A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. This matches the description. The answer is trapezoid.

7. Emma is examining a large rectangular garden. She notices that the garden has two pairs of parallel sides. She then looks at a diamond-shaped kite that has all sides equal in length. The kite has one line of symmetry that goes from the top point to the bottom point. How many lines of symmetry does the kite have? Answer: 1 Solution: Visualize the line of symmetry described - It goes from the top point (vertex) to the bottom point (vertex), splitting the kite into two mirror-image halves.
   Full step-by-step solution

   Step 1: Understand the shape - A kite is a quadrilateral with two pairs of adjacent equal sides. Step 2: Visualize the line of symmetry described - It goes from the top point (vertex) to the bottom point (vertex), splitting the kite into two mirror-image halves. Step 3: Check for other possible lines of symmetry - A typical kite (not a rhombus or square) only has one line of symmetry, which is the one described. The other diagonal (from left to right) would not create matching halves because the sides are not equal on both sides of that line. Step 4: Therefore, the kite has exactly 1 line of symmetry. The answer is 1.

8. 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.