Classifying Quadrilaterals — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. A Grade 4 square has 2 diagonals that are equal and perpendicular.
A square has 2 diagonals; they are congruent and meet at right angles, bisecting each other.
2. In a parallelogram, the diagonals always bisect each other.
Grade 4 fact: in any parallelogram, the diagonals bisect each other, even if they are not equal in length.
3. A rectangle's two diagonals are equal in length.
Rectangle diagonals are congruent because the right angles make the two triangle halves congruent.
4. A rhombus has diagonals that meet at right angles.
In a rhombus, the diagonals are perpendicular, meeting at right angles and bisecting each other.
5. Diagonals of a square are both equal and perpendicular.
A square is both a rectangle and a rhombus, so its diagonals are equal AND perpendicular.
6. Two diagonals of a quadrilateral connect opposite vertices.
A diagonal joins two non-adjacent vertices of a polygon, so a quadrilateral has 2 diagonals.
7. In a kite, exactly one diagonal bisects the other diagonal.
In a kite, the symmetry diagonal bisects the other diagonal at right angles.
8. Diagonals of a non-rectangle parallelogram are usually not equal.
A general parallelogram has diagonals that bisect each other but are usually not congruent unless it is a rectangle.
9. A square's diagonals split it into 4 congruent right triangles.
Because a square has 4 lines of symmetry, its diagonals create 4 congruent right triangles.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
Square (Grade 4)
→ Equal and perpendicular diagonals
Diagonals bisect each other only
Rectangle (non-square)
→ Equal diagonals, not perpendicular
Equal diagonals, not perpendicular
Rhombus (non-square)
→ Perpendicular diagonals, not equal
Perpendicular diagonals, not equal
Parallelogram (general)
→ Diagonals bisect each other only
Equal and perpendicular diagonals
Grade 4 hierarchy: square has equal+perpendicular diagonals; rectangle equal only; rhombus perpendicular only; general parallelogram only bisects.