Geometry: Shapes and Quadrilaterals
Grade 3 · Math · Study Guide
Learn to identify and describe 2D shapes including quadrilaterals, triangles, and polygons.
Geometry is the study of shapes, and in 3rd grade, we learn to describe and classify 2D (flat) shapes by their sides and angles. A polygon is any closed shape made of straight lines.
A quadrilateral is any 4-sided polygon. There are several special quadrilaterals: a rectangle has 4 right angles; a square is a special rectangle with all 4 sides equal; a rhombus has 4 equal sides but angles that are not necessarily right angles; a parallelogram has 2 pairs of parallel sides; and a trapezoid has exactly 1 pair of parallel sides.
Triangles have 3 sides, pentagons have 5, hexagons have 6, and octagons have 8. When you look at a shape, count the sides and look at the angles. Right angles are square corners — like the corner of this page.
Shapes can also be described by their lines of symmetry — an imaginary line you can fold along so both halves match perfectly.
| Shape | Sides | Special Properties |
|---|---|---|
| Square | 4 equal sides | 4 right angles, all sides equal |
| Rectangle | 4 sides | 4 right angles, opposite sides equal |
| Rhombus | 4 equal sides | No right angles required |
| Parallelogram | 4 sides | 2 pairs of parallel sides |
| Trapezoid | 4 sides | Exactly 1 pair of parallel sides |
Key terms
- Polygon
- A closed 2D shape made of straight sides.
- Quadrilateral
- A polygon with exactly 4 sides.
- Right angle
- A 90-degree angle — like the corner of a square or rectangle.
- Parallel lines
- Lines that never meet, always the same distance apart.
- Line of symmetry
- A line that divides a shape into two mirror-image halves.
Flashcards
- Polygon
- Any closed flat shape with straight sides.
- Quadrilateral
- Any 4-sided polygon.
- Parallelogram
- 4-sided shape with 2 pairs of parallel sides.
- Trapezoid
- 4-sided shape with exactly 1 pair of parallel sides.
- Triangle
- 3 sides
- Octagon
- 8 sides — like a stop sign.
Practice questions
How many sides does a hexagon have?
- 5
- 6
- 7
- 8
Show answer
Answer: 6
Hex means six. A hexagon has 6 sides.
A square is a special type of rectangle.
Show answer
Answer: True
A square has 4 right angles like a rectangle, AND all sides are equal. Every square is a rectangle.
A shape with 4 sides is called a ___.
Show answer
Answer: quadrilateral
Quad means four. Any 4-sided polygon is a quadrilateral.
Which shape has exactly 1 pair of parallel sides?
- Square
- Rectangle
- Trapezoid
- Rhombus
Show answer
Answer: Trapezoid
A trapezoid has exactly 1 pair of parallel sides. Squares and rectangles have 2 pairs; rhombuses have 2 pairs.
A triangle, pentagon, and hexagon together have how many sides total?
- 14
- 15
- 16
- 13
Show answer
Answer: 14
Triangle (3) + pentagon (5) + hexagon (6) = 14 sides total.
Fun facts
- A stop sign is an octagon — engineers chose 8 sides so drivers can recognize it from the back even if the color fades!
- Honeybees build their hives in hexagons because that shape uses the least wax to create the most storage space — math in nature!
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