Classify Quadrilaterals

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Answer Key & Explanations

Classify Quadrilaterals · Grade 3 · Worksheet 2

1. Emma is drawing different quadrilaterals in her art book. She draws a shape with 4 sides. All 4 sides are the same length, and all 4 corners are right angles. What is the name of the quadrilateral Emma drew? Answer: square Solution: Identify the properties given: 4 sides, all sides equal length, all angles are right angles (90 degrees). A quadrilateral with these properties is a square. While a rhombus has equal sides, it does not have right angles.
   Full step-by-step solution

   Step 1: Identify the properties given: 4 sides, all sides equal length, all angles are right angles (90 degrees). Step 2: A quadrilateral with these properties is a square. Step 3: While a rhombus has equal sides, it does not have right angles. A rectangle has right angles but not equal sides. A square is the only shape that has both. The answer is a square.

2. Charlotte is drawing a quadrilateral on grid paper. She draws a shape where all four sides are the same length, and all four corners are right angles (90 degrees). Each side measures 9 centimeters. What is the name of the quadrilateral Charlotte is drawing? Answer: square Solution: The shape has 4 sides, so it is a quadrilateral. All four sides are the same length (9 cm each). This means it is not a general rectangle (which can have different side lengths) unless all sides are equal.
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: All four sides are the same length (9 cm each). This means it is not a general rectangle (which can have different side lengths) unless all sides are equal. Step 3: All four corners are right angles (90 degrees). A shape with 4 right angles is a rectangle. Step 4: A rectangle that also has all sides equal is called a square. Step 5: 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.

3. 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.

4. Olivia is drawing a quadrilateral on a geoboard. She makes a shape where all four sides are the same length, measuring 9 centimeters each. When she checks the corners with her square ruler, she finds that none of them are right angles. What type of quadrilateral is Olivia drawing? Answer: rhombus Solution: The shape has 4 sides, so it is a quadrilateral. Step 2: All 4 sides are the same length (9 centimeters each). 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 (9 centimeters each). 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 also have 4 right angles. Olivia's shape does NOT have 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.

5. Hana is drawing different shapes for a geometry project. She draws a quadrilateral with four sides that are all the same length, but its corners are not right angles. What type of quadrilateral did Hana draw? Answer: rhombus Solution: Identify the given properties: the shape has four sides (so it is a quadrilateral). Step 2: The problem says all four sides are the same length. Step 3: The corners are NOT right angles.
   Full step-by-step solution

   Step 1: Identify the given properties: the shape has four sides (so it is a quadrilateral). Step 2: The problem says all four sides are the same length. Step 3: The corners are NOT right angles. Step 4: A shape with four equal sides is a rhombus (or a square, but a square must have right angles). Since the corners are not right angles, it cannot be a square. Step 5: Therefore, the shape is a rhombus.

6. 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.

7. Tane is helping his grandfather build a new garden frame. His grandfather shows him a diagram of a shape with 4 straight sides. All 4 sides are the same length, and all 4 corners are right angles. Which type of quadrilateral is this garden frame? Answer: A) Square|B) Rectangle|C) Rhombus|D) Trapezoid Solution: The shape has 4 sides, so it is a quadrilateral. Step 2: All 4 sides are the same length. Step 3: All 4 corners are right angles (90 degrees).
   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. Step 3: All 4 corners are right angles (90 degrees). Step 4: A square has 4 equal sides and 4 right angles. A rectangle has 4 right angles but not all sides equal. A rhombus has 4 equal sides but not right angles. A trapezoid has only one pair of parallel sides. Therefore, the shape is a square. The correct answer is Square.