Classifying 2D Shapes — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. An equilateral triangle has 3 lines of symmetry.
Each line of symmetry in an equilateral triangle runs from one vertex to the midpoint of the opposite side, and since all three sides are equal, there are 3 such lines.
2. The diagonals of a rhombus cross at right angles.
A special property of every rhombus is that its diagonals always intersect at right angles (90°), even though the diagonals themselves are different lengths.
3. A scalene triangle has 0 line(s) of symmetry.
Because a scalene triangle has no equal sides and no equal angles, there is no way to fold it so that both halves match, giving it zero lines of symmetry.
4. An isosceles triangle has exactly 1 line(s) of symmetry.
An isosceles triangle has two equal sides, so it can only be folded along the line from the vertex between those sides to the midpoint of the base, giving it exactly 1 line of symmetry.
5. A quadrilateral has 2 diagonals.
A quadrilateral has four vertices, and each diagonal connects two non-adjacent vertices, producing exactly 2 diagonals.
6. The number of diagonals in a pentagon is 5.
Using the formula n(n - 3) / 2, a pentagon gives 5(5 - 3) / 2 = 5 diagonals.
7. A regular hexagon has 9 diagonals.
Applying the diagonal formula n(n - 3) / 2 to a hexagon gives 6(6 - 3) / 2 = 9 diagonals.
8. The diagonals of a square are equal in length and bisect each other at right angles.
A square's diagonals are equal in length and cross exactly at their midpoints at 90° angles, so they bisect each other at right angles.
9. An isosceles trapezoid has 1 line(s) of symmetry.
An isosceles trapezoid has two equal non-parallel sides, so it can be folded along one vertical line through the midpoints of both bases, giving it exactly 1 line of symmetry.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each shape to its diagonal property.
Rectangle
→ Diagonals are equal and bisect each other
Diagonals bisect each other but are unequal
Rhombus
→ Diagonals bisect at right angles but are unequal
Diagonals are equal and bisect at right angles
Square
→ Diagonals are equal and bisect at right angles
Diagonals are equal and bisect each other
Parallelogram
→ Diagonals bisect each other but are unequal
Diagonals bisect at right angles but are unequal
Correct matches: Rectangle → Diagonals are equal and bisect each other; Rhombus → Diagonals bisect at right angles but are unequal; Square → Diagonals are equal and bisect at right angles; Parallelogram → Diagonals bisect each other but are unequal.