🎲 Quadrilaterals - 5th Grade Math Complete Notes & Formulae
Quadrilateral: A quadrilateral is a polygon with 4 sides and 4 angles.
1. Parallel Sides in Quadrilaterals
- Parallel sides are sides that run in the same direction and never meet, no matter how far they are extended.
- Many quadrilaterals have parallel sides. For example:
- Many quadrilaterals have parallel sides. For example:
| Quadrilateral | Number of Pairs of Parallel Sides |
|---|---|
| Parallelogram | 2 pairs |
| Rectangle | 2 pairs |
| Rhombus | 2 pairs |
| Square | 2 pairs |
| Trapezoid | 1 pair |
2. Identify Parallelograms
- A parallelogram is a quadrilateral with two pairs of parallel sides.
- The opposite sides are equal & parallel.
- Opposite angles are also equal.
- The opposite sides are equal & parallel.
- Opposite angles are also equal.
AB ∥ CD, AD ∥ BC
AB = CD, AD = BC
AB = CD, AD = BC
3. Identify Trapezoids
- A trapezoid has exactly one pair of parallel sides.
- The parallel sides are called bases.
- The parallel sides are called bases.
Area = \(\frac{1}{2}(b_1 + b_2)h\)
where \(b_1, b_2\) = bases; \(h\) = height
where \(b_1, b_2\) = bases; \(h\) = height
4. Identify Rectangles
- A rectangle is a quadrilateral with 2 pairs of parallel & equal sides.
- All angles = 90°.
- All angles = 90°.
Area = \(l \times w\)
Perimeter = \(2(l + w)\)
Perimeter = \(2(l + w)\)
5. Identify Rhombuses
- A rhombus is a quadrilateral with all sides equal and 2 pairs of parallel sides.
- Opposite angles are equal.
- Diagonals bisect at right angles.
- Opposite angles are equal.
- Diagonals bisect at right angles.
Area = \(\frac{1}{2} \times d_1 \times d_2\)
where \(d_1, d_2\) are diagonal lengths
where \(d_1, d_2\) are diagonal lengths
6. Classify Quadrilaterals
Classification Table:
| Shape | Sides Equal | Parallel Sides | Right Angles? |
|---|---|---|---|
| Square | All 4 | 2 pairs | Yes |
| Rectangle | Opposite sides | 2 pairs | Yes |
| Rhombus | All 4 | 2 pairs | No |
| Parallelogram | Opposite sides | 2 pairs | No |
| Trapezoid | No | 1 pair | No |
| Kite | 2 pairs (adjacent) | None | No |
7. Pick all the Names for a Quadrilateral
- A quadrilateral is any four-sided shape.
- Specific names (like square, rectangle, parallelogram) depend on their sides/angles/parallelism. - Some shapes (like a square) can also be called rectangles and rhombuses because they fit all properties!
- Specific names (like square, rectangle, parallelogram) depend on their sides/angles/parallelism. - Some shapes (like a square) can also be called rectangles and rhombuses because they fit all properties!
8. Draw Quadrilaterals
- Draw using a ruler for straight lines.
- Mark parallel sides with arrow symbols.
- Right angles marked with a square corner □. - All four sides connected, no gaps or overlaps!
- Mark parallel sides with arrow symbols.
- Right angles marked with a square corner □. - All four sides connected, no gaps or overlaps!
9. Identify the Relationships Between Quadrilaterals
- Squares are special rectangles and rhombuses.
- Rectangles, rhombuses, and squares are all parallelograms.
- Parallelograms are all quadrilaterals.
- Trapezoids are not parallelograms (only 1 pair of parallel sides).
Hierarchy Diagram:
Quadrilateral ⟹ Parallelogram ⟹ Rectangle ⟹ Square
Quadrilateral ⟹ Parallelogram ⟹ Rhombus ⟹ Square
Quadrilateral ⟹ Trapezoid
Quadrilateral ⟹ Parallelogram ⟹ Rectangle ⟹ Square
Quadrilateral ⟹ Parallelogram ⟹ Rhombus ⟹ Square
Quadrilateral ⟹ Trapezoid
10. Describe Relationships Among Quadrilaterals
- All the above shapes fit under the "quadrilateral" family.
- Some shapes are subsets of others (a square is a rectangle and a rhombus!). - To describe the relationship, state which shapes include the properties of others.
- Some shapes are subsets of others (a square is a rectangle and a rhombus!). - To describe the relationship, state which shapes include the properties of others.
✅ Key Formulae Recap:
Area of Rectangle: \(A = l \times w\) & Perimeter: \(P = 2(l+w)\)
Area of Square: \(A = s^2\) & Perimeter: \(P = 4s\)
Area of Rhombus: \(A = \frac{1}{2} d_1 d_2\)
Area of Trapezoid: \(A = \frac{1}{2}(b_1 + b_2)h\)
Area of Rectangle: \(A = l \times w\) & Perimeter: \(P = 2(l+w)\)
Area of Square: \(A = s^2\) & Perimeter: \(P = 4s\)
Area of Rhombus: \(A = \frac{1}{2} d_1 d_2\)
Area of Trapezoid: \(A = \frac{1}{2}(b_1 + b_2)h\)