Classify Quadrilaterals

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Classify Quadrilaterals · Grade 3 · Worksheet 1

1. Sophia is helping her grandmother organize a collection of antique tiles. She finds a tile with four sides. Two pairs of opposite sides are parallel, and all four angles are right angles. However, the four sides are not all the same length. What is the best name for this quadrilateral? Answer: rectangle Solution: The tile has 4 sides, so it is a quadrilateral. Step 2: It has two pairs of opposite sides that are parallel. This means it is a parallelogram.
   Full step-by-step solution

   Step 1: The tile has 4 sides, so it is a quadrilateral. Step 2: It has two pairs of opposite sides that are parallel. This means it is a parallelogram. Step 3: All four angles are right angles (90 degrees), which further narrows it down to a rectangle or a square. Step 4: The problem says the four sides are not all the same length. A square requires all sides equal, so it cannot be a square. Step 5: A rectangle has opposite sides equal and all angles right angles, which matches all the clues. The answer is rectangle.

2. Sophia is helping her mom organize a box of tiles for a new bathroom floor. She finds a tile with 4 straight sides and 4 right angles, but only the opposite sides are equal in length. Which type of quadrilateral is this tile? Answer: D. Rectangle Solution: The tile has 4 straight sides, so it is a quadrilateral. Step 2: It has 4 right angles (90-degree corners). A square and a rectangle both have 4 right angles.
   Full step-by-step solution

   Step 1: The tile has 4 straight sides, so it is a quadrilateral. Step 2: It has 4 right angles (90-degree corners). A square and a rectangle both have 4 right angles. Step 3: But only the opposite sides are equal in length — not all four sides. A square has all four sides equal, so this cannot be a square. Step 4: A rectangle has opposite sides equal and 4 right angles, so this matches perfectly. Step 5: A rhombus has equal sides but not necessarily right angles, and a trapezoid has only one pair of parallel sides. Therefore, the correct answer is Rectangle.

3. Mason is helping his grandmother sort through a box of old wooden puzzle pieces. He finds a piece with four straight sides. He measures the sides and finds that all four sides are exactly 7 inches long. He also notices that all four corners are right angles, just like the corners of a book. What is the special name for this type of quadrilateral? Answer: square Solution: The piece has 4 sides, so it is a quadrilateral. All four sides are the same length (7 inches). All four corners are right angles (90 degrees).
   Full step-by-step solution

   Step 1: The piece has 4 sides, so it is a quadrilateral. Step 2: All four sides are the same length (7 inches). Step 3: All four corners are right angles (90 degrees). Step 4: A quadrilateral with 4 equal sides and 4 right angles is called a square. The answer is square.

4. Aroha is helping her grandmother organize a box of old buttons. She finds a button with 4 equal sides and 4 right angles. What is the best name for this shape? Answer: square Solution: The button has 4 sides, so it is a quadrilateral. Step 2: The button has 4 equal sides. Step 3: The button has 4 right angles (like the corner of a square).
   Full step-by-step solution

   Step 1: The button has 4 sides, so it is a quadrilateral. Step 2: The button has 4 equal sides. Step 3: The button has 4 right angles (like the corner of a square). Step 4: A quadrilateral with 4 equal sides and 4 right angles is called a square. The answer is a square.

5. Emma drew a quadrilateral with 4 sides. Two of the sides are parallel, and the other two sides are not parallel. The shape has no right angles. What type of quadrilateral did Emma draw? Answer: trapezoid Solution: Identify the key properties from the problem: The shape has 4 sides (so it is a quadrilateral). Two sides are parallel, and the other two are not parallel. There are no right angles.
   Full step-by-step solution

   Step 1: Identify the key properties from the problem: The shape has 4 sides (so it is a quadrilateral). Two sides are parallel, and the other two are not parallel. There are no right angles. Step 2: Recall the definitions: A trapezoid has exactly one pair of parallel sides. A parallelogram, rectangle, rhombus, and square all have two pairs of parallel sides. Step 3: Since this shape has only one pair of parallel sides and no right angles, it must be a trapezoid. The answer is trapezoid.

6. 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.

7. Kaia is designing a quilt for her grandmother's 60th birthday. She draws a shape with 4 straight sides. All 4 sides are the same length, but none of the angles are right angles. What type of quadrilateral is Kaia drawing? Answer: rhombus Solution: Identify the properties given in the problem. The shape has 4 straight sides, so it is a quadrilateral. All 4 sides are the same length.
   Full step-by-step solution

   Step 1: Identify the properties given in the problem. The shape has 4 straight sides, so it is a quadrilateral. All 4 sides are the same length. None of the angles are right angles (not 90 degrees). Step 2: Think about quadrilaterals with equal sides. A square has 4 equal sides AND 4 right angles. Since the angles are not right angles, it cannot be a square. A rhombus has 4 equal sides but does not require right angles. Therefore, the shape must be a rhombus. The answer is a rhombus.

8. Mati has a quadrilateral where all four sides are 60 centimeters long. He checks the corners and finds that two opposite corners are smaller than the corner of a book, and the other two opposite corners are larger than the corner of a book. What type of quadrilateral is Mati describing? Answer: rhombus Solution: The shape has 4 sides, so it is a quadrilateral. All 4 sides are the same length (60 cm). This means it is not a general trapezoid or parallelogram (which can have different side lengths).
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: All 4 sides are the same length (60 cm). This means it is not a general trapezoid or parallelogram (which can have different side lengths). Step 3: A square also has 4 equal sides, but a square must have 4 right angles (exactly like the corner of a book). Mati's shape does NOT have any right angles. Step 4: The only quadrilateral with 4 equal sides that does NOT have to have right angles is a rhombus. The answer is a rhombus.