Classify Quadrilaterals

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Answer Key & Explanations

Classify Quadrilaterals · Grade 3 · Worksheet 1

1. Sophia is drawing different quadrilaterals in her art class. She draws a shape with 4 sides where opposite sides are parallel and all four sides are the same length, but the corners are not right angles. What type of quadrilateral did Sophia draw? Answer: Rhombus Solution: Recall the properties of a rhombus: all four sides are equal in length, opposite sides are parallel, but angles are not necessarily 90 degrees.
   Full step-by-step solution

   Step 1: Recall the properties of a rhombus: all four sides are equal in length, opposite sides are parallel, but angles are not necessarily 90 degrees. Step 2: Compare with other quadrilaterals: a square has equal sides and right angles; a rectangle has opposite sides equal and right angles; a trapezoid has only one pair of parallel sides; a parallelogram has opposite sides parallel but sides may not be equal. Step 3: Since the shape has equal sides and opposite sides parallel without right angles, it matches the definition of a rhombus. The answer is a rhombus.

2. Mason is designing a quilt with different fabric pieces. He has one piece with 4 equal sides and 4 right angles. His grandmother says, 'That sounds like a square, but is it also a rectangle?' Mason is confused. Can you help him? Is a square also a rectangle? Answer: Yes, a square is also a rectangle. Solution: Remember the definition of a rectangle: a quadrilateral (4-sided shape) with 4 right angles. Remember the definition of a square: a quadrilateral with 4 right angles AND 4 equal sides. Compare the two.
   Full step-by-step solution

   Step 1: Remember the definition of a rectangle: a quadrilateral (4-sided shape) with 4 right angles. Step 2: Remember the definition of a square: a quadrilateral with 4 right angles AND 4 equal sides. Step 3: Compare the two. A square has 4 right angles, which is the main rule for being a rectangle. Step 4: Since the square follows all the rules of a rectangle, it is included in the rectangle family. The answer is: Yes, a square is also a rectangle.

3. Mason is helping his dad build a sandbox for the backyard. His dad drew a shape with 4 sides where only one pair of opposite sides are parallel. What type of quadrilateral is the sandbox shape? Answer: trapezoid Solution: Recognize that a sandbox shape with 4 sides is a quadrilateral. The clue says only one pair of opposite sides are parallel. A square has two pairs of parallel sides, so it is not correct.
   Full step-by-step solution

   Step 1: Recognize that a sandbox shape with 4 sides is a quadrilateral. Step 2: The clue says only one pair of opposite sides are parallel. Step 3: A square has two pairs of parallel sides, so it is not correct. Step 4: A rectangle also has two pairs of parallel sides, so it is not correct. Step 5: A parallelogram has two pairs of parallel sides, so it is not correct. Step 6: A rhombus has all sides equal but also has two pairs of parallel sides, so it is not correct. Step 7: A trapezoid has exactly one pair of opposite sides parallel, which matches the clue. The answer is trapezoid.

4. Charlotte is drawing a quadrilateral on a geoboard. She says her shape has 4 sides, all sides are the same length, and it has 4 right angles. Isabella says, "That sounds like a square!" Mason says, "It could also be called a rhombus." Who is correct? Explain your reasoning using the properties of quadrilaterals. Answer: Both Isabella and Mason are correct. A square is a special type of rhombus because it has 4 equal sides (a property of a rhombus) AND 4 right angles. So the shape is a square, and all squares are also rhombuses. Solution: List the properties given: 4 sides (quadrilateral), all sides equal, 4 right angles. A square is defined as a quadrilateral with 4 equal sides and 4 right angles. The shape matches this exactly, so it is a square.
   Full step-by-step solution

   Step 1: List the properties given: 4 sides (quadrilateral), all sides equal, 4 right angles. Step 2: A square is defined as a quadrilateral with 4 equal sides and 4 right angles. The shape matches this exactly, so it is a square. Isabella is correct. Step 3: A rhombus is defined as a quadrilateral with 4 equal sides. It does NOT require right angles. The shape has 4 equal sides, so it fits the definition of a rhombus. Mason is also correct. Step 4: A square is a special type of rhombus (a rhombus with right angles). Therefore, both Isabella and Mason are correct. The shape is a square, and every square is also a rhombus.

5. Tane is helping his grandmother sort a box of old wooden tiles for a craft project. He finds a tile with 4 sides. The tile has opposite sides that are parallel, but the sides are not all the same length, and the corners are not right angles. Which type of quadrilateral is this tile? Answer: parallelogram Solution: The tile has 4 sides, so it is a quadrilateral. Step 2: Opposite sides are parallel. Step 3: It does not have right angles, so it is not a square or a rectangle.
   Full step-by-step solution

   Step 1: The tile has 4 sides, so it is a quadrilateral. Step 2: Opposite sides are parallel. Step 3: It does not have right angles, so it is not a square or a rectangle. Step 4: The sides are not all equal, so it is not a rhombus. Step 5: A trapezoid has only one pair of parallel sides, but this tile has two pairs. Step 6: A parallelogram has two pairs of parallel sides and does not require equal sides or right angles. Therefore, the tile is a parallelogram.

6. Hana is drawing a quadrilateral with 4 equal sides. She measures one side and finds it is 12 centimeters long. She also notices that all four corners are right angles. What is the name of the quadrilateral Hana is drawing? Answer: square Solution: Identify the properties given: 4 equal sides (all sides are 12 cm) and 4 right angles. A shape with 4 equal sides is either a square or a rhombus. A shape with 4 right angles is either a square or a rectangle.
   Full step-by-step solution

   Step 1: Identify the properties given: 4 equal sides (all sides are 12 cm) and 4 right angles. Step 2: A shape with 4 equal sides is either a square or a rhombus. Step 3: A shape with 4 right angles is either a square or a rectangle. Step 4: The only shape that has BOTH 4 equal sides AND 4 right angles is a square. Step 5: Therefore, the quadrilateral Hana is drawing is a square.

7. Isabella is helping her grandmother organize a collection of vintage tiles. She finds a tile with four sides. Two sides are parallel, but the other two sides are not parallel. Which type of quadrilateral is Isabella's tile? Answer: trapezoid Solution: Recall the definitions of quadrilaterals. A trapezoid is a quadrilateral with exactly one pair of parallel sides. Step 2: Isabella's tile has four sides and only two sides that are parallel, which matches the definition of a trapezoid.
   Full step-by-step solution

   Step 1: Recall the definitions of quadrilaterals. A trapezoid is a quadrilateral with exactly one pair of parallel sides. Step 2: Isabella's tile has four sides and only two sides that are parallel, which matches the definition of a trapezoid. Step 3: Other quadrilaterals like squares, rectangles, and parallelograms all have two pairs of parallel sides, so they do not fit. The answer is trapezoid.

8. Sophia is drawing a quadrilateral on a geoboard. She makes a shape with all four sides equal in length, but its angles are NOT right angles. One pair of opposite angles is acute (less than 90 degrees) and the other pair is obtuse (more than 90 degrees). What specific type of quadrilateral did Sophia draw? Answer: Rhombus Solution: Identify the properties given. The shape has 4 equal sides. This means it is either a square or a rhombus.
   Full step-by-step solution

   Step 1: Identify the properties given. The shape has 4 equal sides. This means it is either a square or a rhombus. Step 2: The angles are NOT right angles. A square must have four right angles (90 degrees each). Since this shape does not have right angles, it cannot be a square. Step 3: A rhombus is defined as a quadrilateral with all four sides equal in length. Its angles can vary; they do not have to be 90 degrees. This perfectly matches the description. Step 4: Therefore, the quadrilateral Sophia drew is a rhombus. The answer is Rhombus.