Classify Quadrilaterals

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Answer Key & Explanations

Classify Quadrilaterals · Grade 3 · Worksheet 2

1. Mere is drawing a quadrilateral with these properties: - All 4 sides are equal in length - It has 4 right angles (90 degrees each) - Opposite sides are parallel What is the name of the quadrilateral Mere is drawing? Answer: square Solution: Identify the properties given: all 4 sides equal, 4 right angles, opposite sides parallel. A shape with 4 right angles is a rectangle. A rectangle with all sides equal is called a square.
   Full step-by-step solution

   Step 1: Identify the properties given: all 4 sides equal, 4 right angles, opposite sides parallel. Step 2: A shape with 4 right angles is a rectangle. Step 3: A rectangle with all sides equal is called a square. Step 4: Check: Does a square have all these properties? Yes - a square has 4 equal sides, 4 right angles, and opposite sides are parallel. The answer is square.

2. Mason is drawing a quadrilateral on a geoboard. He says, 'My shape has exactly one pair of parallel sides, and the other two sides are not parallel.' What type of quadrilateral is Mason describing? Answer: Trapezoid Solution: Remember that quadrilaterals are shapes with four sides. Step 2: The clue says the shape has exactly one pair of parallel sides. Step 3: A square has two pairs of parallel sides, so it is not a square.
   Full step-by-step solution

   Step 1: Remember that quadrilaterals are shapes with four sides. Step 2: The clue says the shape has exactly one pair of parallel sides. Step 3: A square has two pairs of parallel sides, so it is not a square. Step 4: A rectangle has two pairs of parallel sides, so it is not a rectangle. Step 5: A parallelogram has two pairs of parallel sides, so it is not a parallelogram. Step 6: A rhombus has two pairs of parallel sides, so it is not a rhombus. Step 7: A trapezoid has exactly one pair of parallel sides. This matches the clue. The answer is a trapezoid.

3. Sophia is helping her grandmother organize a box of old buttons. She finds a button with 4 sides. Two pairs of sides are parallel, but the sides are not all the same length, and the corners are not right angles. Which type of quadrilateral is this button? Answer: parallelogram Solution: Identify the clues - 4 sides, two pairs of parallel sides, not all sides equal, no right angles. A square has 4 equal sides and 4 right angles, so this is not a square.
   Full step-by-step solution

   Step 1: Identify the clues - 4 sides, two pairs of parallel sides, not all sides equal, no right angles. Step 2: A square has 4 equal sides and 4 right angles, so this is not a square. Step 3: A rectangle has opposite sides equal and 4 right angles, so this is not a rectangle. Step 4: A rhombus has 4 equal sides but no right angles - this button does not have all equal sides. Step 5: A trapezoid has only one pair of parallel sides, but this button has two pairs. Step 6: A parallelogram has two pairs of parallel sides, does not require right angles, and opposite sides are equal but not all sides are equal. This matches all clues. The answer is parallelogram.

4. Ava is drawing a quadrilateral with 4 sides of equal length. She measures each side and finds it is 6 centimeters long. However, when she checks the corners, none of them are right angles. What type of quadrilateral is Ava drawing? Answer: rhombus Solution: Identify the properties given: 4 equal sides, each 6 cm long. Step 2: Check if it could be a square: A square has 4 equal sides AND 4 right angles. Since the corners are not right angles, it is not a square.
   Full step-by-step solution

   Step 1: Identify the properties given: 4 equal sides, each 6 cm long. Step 2: Check if it could be a square: A square has 4 equal sides AND 4 right angles. Since the corners are not right angles, it is not a square. Step 3: Consider a rhombus: A rhombus has 4 equal sides, and its angles do not have to be 90 degrees. Step 4: Therefore, Ava is drawing a rhombus.

5. Mason is drawing a quadrilateral on his geoboard. He says his shape has 4 sides and 4 right angles. Charlotte says it could be a square or a rectangle. Isabella says if all 4 sides are 7 inches long, then it must be a square. What is the name of a quadrilateral that has 4 equal sides and 4 right angles? Answer: square Solution: The shape has 4 sides, so it is a quadrilateral. Step 2: It has 4 right angles, so it could be a square or a rectangle. Step 3: It also has all 4 sides equal in length (7 inches each).
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: It has 4 right angles, so it could be a square or a rectangle. Step 3: It also has all 4 sides equal in length (7 inches each). Step 4: A rectangle has opposite sides equal, but not all 4 sides equal. A square has all 4 sides equal and all 4 right angles. The answer is a square.

6. Liam is drawing shapes for a geometry art project. He draws a quadrilateral where all four sides are the same length, but the angles are not 90 degrees. What type of quadrilateral did Liam draw? Answer: rhombus Solution: Remember that a quadrilateral has four sides. Step 2: The problem says all four sides are the same length. This means it could be a square or a rhombus.
   Full step-by-step solution

   Step 1: Remember that a quadrilateral has four sides. Step 2: The problem says all four sides are the same length. This means it could be a square or a rhombus. Step 3: The problem also says the angles are NOT 90 degrees. A square always has 90-degree angles, so it cannot be a square. Step 4: A rhombus has equal sides but can have angles that are not 90 degrees. Therefore, the shape is a rhombus.

7. Emma is drawing different shapes on her geoboard. She makes a shape with 4 sides. All 4 sides are the same length, but none of the corners are right angles. Emma says, 'This shape is a square.' Is Emma correct? What quadrilateral has she actually drawn? Answer: No, it is a rhombus Solution: A square must have two important properties: all 4 sides equal AND all 4 angles are right angles (90 degrees). Step 2: Emma's shape has all 4 sides equal, which matches a square.
   Full step-by-step solution

   Step 1: A square must have two important properties: all 4 sides equal AND all 4 angles are right angles (90 degrees). Step 2: Emma's shape has all 4 sides equal, which matches a square. Step 3: However, her shape does NOT have right angles. This means it cannot be a square. Step 4: A quadrilateral with 4 equal sides but angles that are not right angles is called a rhombus. Step 5: So Emma is incorrect; she has drawn a rhombus, not a square.

8. Olivia is drawing a quadrilateral on her driveway with chalk. She draws a shape with 4 sides. Opposite sides are parallel, and all four angles are right angles. However, not all sides are the same length. What type of quadrilateral did Olivia draw? Answer: rectangle Solution: The shape has 4 sides, so it is a quadrilateral. It has 4 right angles (like the corner of a piece of paper). Opposite sides are parallel, meaning the top and bottom are parallel, and the left and right are parallel.
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: It has 4 right angles (like the corner of a piece of paper). Step 3: Opposite sides are parallel, meaning the top and bottom are parallel, and the left and right are parallel. Step 4: Not all sides are the same length, so it cannot be a square (which has all sides equal). Step 5: A rectangle has all these properties: 4 right angles, opposite sides parallel and equal, but sides can be different lengths. The answer is a rectangle.