Classify 2D Shapes

lessonbunny.com

Answer Key & Explanations

Classify 2D Shapes · Grade 4 · Worksheet 2

1. 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.

2. Isabella is designing a large rectangular garden for her grandmother. The garden has two pairs of parallel sides and four right angles. Isabella wants to place a fence along one of the lines of symmetry of the rectangle. The rectangle is 127 feet long and 72 feet wide. How many lines of symmetry does this rectangle have? Answer: 2 Solution: Recall that a line of symmetry divides a shape into two identical mirror-image halves. A rectangle has opposite sides that are parallel and equal. This rectangle is 127 feet long and 72 feet wide.
   Full step-by-step solution

   Step 1: Recall that a line of symmetry divides a shape into two identical mirror-image halves. Step 2: A rectangle has opposite sides that are parallel and equal. This rectangle is 127 feet long and 72 feet wide. Step 3: Fold the rectangle vertically down the middle. The left half (36 feet wide) matches the right half (36 feet wide) perfectly, so this is one line of symmetry. Step 4: Fold the rectangle horizontally across the middle. The top half (63.5 feet long) matches the bottom half (63.5 feet long) perfectly, so this is a second line of symmetry. Step 5: Diagonal folds do not work because the sides are different lengths—a diagonal fold would not create matching halves. Step 6: Since this rectangle is not a square (which has four lines of symmetry), it has exactly two lines of symmetry. The answer is 2.

3. Mere is designing a large tile pattern for the floor of a new community hall. She draws a shape with exactly 4 sides. Opposite sides are parallel and equal in length, and all four angles are right angles. The length of the tile is 125 centimeters and the width is 80 centimeters. Does this shape have any lines of symmetry? If so, how many? Answer: Yes, it has 2 lines of symmetry. Solution: Identify the shape. A quadrilateral with opposite sides parallel and equal, and four right angles, is a rectangle. The left half (62.5 cm wide) matches the right half (62.5 cm wide) perfectly.
   Full step-by-step solution

   Step 1: Identify the shape. A quadrilateral with opposite sides parallel and equal, and four right angles, is a rectangle. Step 2: A rectangle has two lines of symmetry: one vertical line through the middle and one horizontal line through the middle. Step 3: Check the vertical line: fold from top to bottom through the center. The left half (62.5 cm wide) matches the right half (62.5 cm wide) perfectly. Step 4: Check the horizontal line: fold from left to right through the center. The top half (40 cm tall) matches the bottom half (40 cm tall) perfectly. Step 5: Diagonal lines do not work because the sides are different lengths (125 cm and 80 cm), so a diagonal fold would not create matching halves. Step 6: Therefore, the rectangle has exactly 2 lines of symmetry. The answer is: Yes, it has 2 lines of symmetry.

4. Noah is examining a large rectangular garden that has a decorative path cutting across it from one corner to the opposite corner. The garden is 12 meters long and 7 meters wide. The path splits the rectangle into two congruent triangles. How many pairs of parallel sides does the original rectangular garden have? Answer: 2 Solution: Recall that a rectangle is a quadrilateral with four right angles. In a rectangle, opposite sides are parallel to each other. The rectangle has two pairs of opposite sides: the two longer sides (12 m each) are parallel, and the two shorter sides (7 m each) are parallel.
   Full step-by-step solution

   Step 1: Recall that a rectangle is a quadrilateral with four right angles. Step 2: In a rectangle, opposite sides are parallel to each other. Step 3: The rectangle has two pairs of opposite sides: the two longer sides (12 m each) are parallel, and the two shorter sides (7 m each) are parallel. Step 4: Therefore, the garden has 2 pairs of parallel sides. The answer is 2.

5. Emma draws a shape with 4 sides. Two pairs of opposite sides are parallel, but the sides are not all the same length, and the angles are not all right angles. Which shape did Emma draw? Answer: parallelogram Solution: Identify the shape has 4 sides, so it is a quadrilateral. Two pairs of opposite sides are parallel. This means it is a parallelogram.
   Full step-by-step solution

   Step 1: Identify the shape has 4 sides, so it is a quadrilateral. Step 2: Two pairs of opposite sides are parallel. This means it is a parallelogram. Step 3: The sides are not all the same length, so it is not a rhombus (which has all sides equal). Step 4: The angles are not all right angles, so it is not a rectangle (which has four right angles). Step 5: The only shape that fits all clues is a parallelogram. The answer is parallelogram.