Classifying Quadrilaterals — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A trapezoid has two pairs of parallel sides in Grade 4 geometry.
Corrected: A trapezoid has one pair of parallel sides in Grade 4 geometry.
Grade 4 students learn a trapezoid has exactly one pair of parallel sides; two pairs would make it a parallelogram.
2. Fix the sentence:
An isosceles trapezoid have two congruent non-parallel sides.
Corrected: An isosceles trapezoid has two congruent non-parallel sides.
Grade 4 grammar requires 'has' with the singular subject 'trapezoid'; 'isosceles' tells you the legs are congruent.
3. Fix the sentence:
Each trapezoid have four vertices and one pair of parallel sides.
Corrected: Each trapezoid has four vertices and one pair of parallel sides.
In Grade 4, every quadrilateral has four vertices, and a trapezoid is named for its single pair of parallel sides.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A Grade 4 trapezoid has exactly one pair of parallel sides.
Trapezoids are defined in Grade 4 by having exactly one pair of parallel sides.
2. Every quadrilateral, including a trapezoid, has four vertices.
Grade 4 students learn that every quadrilateral has four vertices and four sides.
3. An isosceles trapezoid has two congruent non-parallel legs.
Grade 4 vocabulary: an isosceles trapezoid has congruent legs, giving it one line of symmetry.
4. The two parallel sides of a trapezoid are called bases.
Grade 4 geometry names the parallel sides of a trapezoid the bases; the other two sides are the legs.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why a square is not a trapezoid in the Grade 4 classification used at school.
Sample answer: A square has two pairs of parallel sides, but a trapezoid in Grade 4 has only one pair. Because a square has more, it is classified as a parallelogram, not a trapezoid.
Grade 4 uses the exclusive definition of a trapezoid: exactly one pair of parallel sides.
2. Describe one attribute that makes an isosceles trapezoid special compared with other Grade 4 trapezoids.
Sample answer: An isosceles trapezoid has two congruent legs, so its non-parallel sides are equal in length. This gives it one line of symmetry, unlike most trapezoids.
Grade 4 students recognize isosceles trapezoids by congruent legs and a single line of symmetry.