Classify 2D Shapes

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Answer Key & Explanations

Classify 2D Shapes · Grade 4 · Worksheet 1

1. Mason is designing a stained glass window for a community center. The window will be made of two shapes: a parallelogram and a trapezoid. The parallelogram has two pairs of parallel sides. The trapezoid has exactly one pair of parallel sides. Mason wants to add a line of symmetry to the trapezoid by making it an isosceles trapezoid. How many pairs of parallel sides does an isosceles trapezoid have? Answer: 1 Solution: Recall the definition of a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is a special type of trapezoid where the non-parallel sides (legs) are equal in length.
   Full step-by-step solution

   Step 1: Recall the definition of a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides. Step 2: An isosceles trapezoid is a special type of trapezoid where the non-parallel sides (legs) are equal in length. This does not change the number of parallel sides. Step 3: Therefore, an isosceles trapezoid still has exactly one pair of parallel sides. The answer is 1.

2. Hana is drawing a quadrilateral with exactly one pair of parallel sides. She has already drawn three sides. The top side is 12 cm long, the bottom side is 18 cm long, and the left side is 10 cm long and slanted. What is the name of the shape Hana is drawing? Answer: trapezoid Solution: Hana is drawing a quadrilateral, which is a shape with four sides. Step 2: The key property is 'exactly one pair of parallel sides.' Step 3: A parallelogram has two pairs of parallel sides, so it does not fit.
   Full step-by-step solution

   Step 1: Hana is drawing a quadrilateral, which is a shape with four sides. Step 2: The key property is 'exactly one pair of parallel sides.' Step 3: A parallelogram has two pairs of parallel sides, so it does not fit. A trapezoid (or trapezium) has exactly one pair of parallel sides. Step 4: Therefore, the shape Hana is drawing is a trapezoid. The answer is trapezoid.

3. Charlotte is helping her younger brother sort a box of 2D shape tiles. She finds a tile with 4 sides, where exactly one pair of opposite sides is parallel. The tile also has 2 acute angles and 2 obtuse angles. What is the name of this shape? Answer: trapezoid Solution: Identify the shape has 4 sides, so it is a quadrilateral. The shape has exactly one pair of parallel sides. This rules out squares, rectangles, rhombuses, and parallelograms (which have two pairs of parallel sides).
   Full step-by-step solution

   Step 1: Identify the shape has 4 sides, so it is a quadrilateral. Step 2: The shape has exactly one pair of parallel sides. This rules out squares, rectangles, rhombuses, and parallelograms (which have two pairs of parallel sides). Step 3: The shape has 2 acute and 2 obtuse angles, which is common for a trapezoid that is not isosceles. Step 4: A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. This matches the description. The answer is trapezoid.

4. A quadrilateral has 3 pairs of parallel sides and 3 right angles. Is this shape possible? Explain. Answer: No Solution: A quadrilateral has 4 sides. The maximum number of pairs of parallel sides in a quadrilateral is 2 (in a parallelogram or rectangle). Having 3 pairs is impossible because that would require at least 6 sides.
   Full step-by-step solution

   Step 1: A quadrilateral has 4 sides. The maximum number of pairs of parallel sides in a quadrilateral is 2 (in a parallelogram or rectangle). Having 3 pairs is impossible because that would require at least 6 sides. Step 2: A quadrilateral has 4 angles. If 3 are right angles (90° each), that's 270°. The sum of all angles in a quadrilateral is 360°, so the fourth angle would be 360° - 270° = 90°. That means all 4 angles would be 90°, which is possible for a rectangle. However, the first condition (3 pairs of parallel sides) is impossible. Therefore, the shape is not possible. The answer is No.

5. Aroha is drawing a large mosaic pattern for her school's art project. She draws a shape with exactly 4 sides. Two pairs of sides are parallel to each other, and all four sides are the same length. However, none of the corners are square corners (right angles). What is the name of the shape Aroha has drawn? Answer: rhombus Solution: The shape has 4 sides, so it is a quadrilateral. It has two pairs of parallel sides, so it is a parallelogram. All four sides are the same length, so it is a rhombus.
   Full step-by-step solution

   Step 1: The shape has 4 sides, so it is a quadrilateral. Step 2: It has two pairs of parallel sides, so it is a parallelogram. Step 3: All four sides are the same length, so it is a rhombus. Step 4: It does not have right angles, so it cannot be a square. Therefore, the shape is a rhombus.

6. Isabella is looking at a large decorative tile in the shape of a regular octagon. The tile has 8 equal sides and 8 equal angles. How many lines of symmetry does this shape have? Answer: 8 Solution: A regular octagon has 8 equal sides and 8 equal angles. For any regular polygon, the number of lines of symmetry equals the number of sides if the number of sides is even.
   Full step-by-step solution

   Step 1: A regular octagon has 8 equal sides and 8 equal angles. Step 2: For any regular polygon, the number of lines of symmetry equals the number of sides if the number of sides is even. Step 3: Since an octagon has 8 sides, it has 8 lines of symmetry. Step 4: These lines go through opposite vertices (4 lines) and through the midpoints of opposite sides (4 lines). Step 5: So, the total is 4 + 4 = 8 lines of symmetry. Answer: 8

7. Sophia is drawing a large quadrilateral on a piece of paper. She draws it so that two of its sides are always the same distance apart and never meet, even if they were extended. The other two sides are not parallel to each other. This shape has exactly one line of symmetry that goes through the middle of the two parallel sides. What is the name of the quadrilateral Sophia is drawing? Answer: isosceles trapezoid Solution: Identify the properties given. The shape has two sides that are always the same distance apart (parallel). The other two sides are not parallel.
   Full step-by-step solution

   Step 1: Identify the properties given. The shape has two sides that are always the same distance apart (parallel). The other two sides are not parallel. This means the shape is a trapezoid (a quadrilateral with exactly one pair of parallel sides). Step 2: The shape has exactly one line of symmetry. A line of symmetry divides a shape into two mirror-image halves. A regular trapezoid (with non-equal legs) has no lines of symmetry. Step 3: A trapezoid with one line of symmetry must have its two non-parallel sides equal in length. This special type of trapezoid is called an isosceles trapezoid. The line of symmetry runs through the midpoints of the two parallel sides. Step 4: Therefore, the quadrilateral is an isosceles trapezoid.