📐 Geometry - Grade 3
Understanding Geometry!
Geometry is the study of shapes, sizes, positions, and properties of things around us! Let's explore 2D shapes, 3D shapes, and more!
📏 Identify Two-Dimensional Shapes
What are 2D Shapes?
Two-dimensional (2D) shapes are flat shapes that have only two dimensions: length and width. They have no thickness or depth!
2D shapes are also called flat shapes or plane shapes.
Common 2D Shapes:
Shape Name | Number of Sides | Properties |
---|---|---|
Circle ⭕ | 0 (curved) | Round, no corners |
Triangle 🔺 | 3 | 3 sides, 3 corners |
Square 🟦 | 4 | 4 equal sides, 4 right angles |
Rectangle 🟥 | 4 | Opposite sides equal, 4 right angles |
Pentagon | 5 | 5 sides, 5 corners |
Hexagon | 6 | 6 sides, 6 corners |
Octagon | 8 | 8 sides, 8 corners (like STOP sign) |
🔢 Count and Compare Sides and Vertices
Important Terms:
• Side: A straight line that forms part of a shape
• Vertex (plural: Vertices): A corner where two sides meet
• Angle: The space between two sides at a vertex
Counting Rule:
Number of Sides = Number of Vertices = Number of Angles
(For all polygons)
Examples:
Triangle: 3 sides, 3 vertices, 3 angles
Square: 4 sides, 4 vertices, 4 angles
Pentagon: 5 sides, 5 vertices, 5 angles
Hexagon: 6 sides, 6 vertices, 6 angles
Octagon: 8 sides, 8 vertices, 8 angles
💡 Tip: To count sides, trace around the shape. To count vertices, count the corners!
📦 Identify Three-Dimensional Shapes
What are 3D Shapes?
Three-dimensional (3D) shapes are solid shapes that have three dimensions: length, width, and height (depth)!
3D shapes are also called solid shapes. You can hold them in your hand!
Common 3D Shapes:
Shape Name | Faces | Edges | Vertices | Example |
---|---|---|---|---|
Sphere | 1 curved | 0 | 0 | Ball, globe |
Cube | 6 | 12 | 8 | Dice, Rubik's cube |
Cuboid | 6 | 12 | 8 | Box, book |
Cylinder | 3 (2 flat, 1 curved) | 2 | 0 | Can, pipe |
Cone | 2 (1 flat, 1 curved) | 1 | 1 | Ice cream cone, party hat |
Pyramid | 5 | 8 | 5 | Egyptian pyramid, tent |
🔢 Count Vertices, Edges and Faces
Important 3D Terms:
• Face: A flat surface of a 3D shape
• Edge: A line where two faces meet
• Vertex (Vertices): A corner where edges meet
Euler's Formula for 3D Shapes:
\(\text{Faces} + \text{Vertices} = \text{Edges} + 2\)
\(F + V = E + 2\)
Example: Cube
Faces: 6 (all squares)
Vertices: 8 (corners)
Edges: 12 (lines where faces meet)
Check with Euler's Formula:
\(6 + 8 = 12 + 2\)
\(14 = 14\) ✓
🎲 Identify Faces of Three-Dimensional Shapes
What are Faces?
Faces are the flat or curved surfaces of a 3D shape. Each face is a 2D shape!
Examples:
Cube:
All 6 faces are squares
Cuboid (Rectangular Prism):
All 6 faces are rectangles
Cylinder:
2 faces are circles (top and bottom)
1 face is curved (side)
Square Pyramid:
1 face is a square (base)
4 faces are triangles (sides)
⬡ Is It a Polygon?
What is a Polygon?
A polygon is a closed 2D shape made up of straight line segments!
Rules for a Polygon:
- Must be CLOSED - All sides connect
- Must have STRAIGHT sides - No curves
- Must have at least 3 sides - Minimum is a triangle
- Sides can only touch at vertices - Lines don't cross
Polygons vs Non-Polygons:
Polygons ✓ | NOT Polygons ✗ |
---|---|
Triangle, Square, Rectangle | Circle (curved) |
Pentagon, Hexagon, Octagon | Oval (curved) |
All sides are straight | Open shapes (not closed) |
Completely closed | Shapes with curved sides |
🔄 Reflection, Rotation and Translation
What are Transformations?
Transformations are ways to move or change the position of a shape!
Three Types of Transformations:
1. Reflection (Flip) 🪞
Reflection means flipping a shape over a line (like a mirror)!
• The shape stays the same size
• It flips to the opposite side
• Like looking in a mirror
• Example: Flip a letter "b" to get "d"
2. Rotation (Turn) 🔄
Rotation means turning a shape around a point!
• The shape stays the same size
• It turns around a center point
• Can turn 90°, 180°, 270°, or 360°
• Example: Turn a square 90° (quarter turn)
3. Translation (Slide) ➡️
Translation means sliding a shape to a new position!
• The shape stays the same size
• It moves in a straight line
• Can move up, down, left, or right
• Example: Slide a triangle 3 units right
💡 Remember: All transformations keep the shape the same size and form!
🦋 Symmetry
What is Symmetry?
A shape has symmetry when one half is a mirror image of the other half!
The imaginary line that divides the shape into two equal halves is called the line of symmetry.
Lines of Symmetry in Shapes:
Shape | Lines of Symmetry |
---|---|
Circle | Infinite (countless) |
Square | 4 |
Rectangle | 2 |
Equilateral Triangle | 3 |
Regular Pentagon | 5 |
Regular Hexagon | 6 |
How to Test for Symmetry:
- Fold the shape in half (or imagine folding)
- Check if both halves match perfectly
- If they match, it has symmetry!
- The fold line is the line of symmetry
🗺️ Maps
What are Maps in Geometry?
In geometry, maps help us locate shapes and objects using coordinates or directions!
Grid Coordinates:
Maps use a grid with rows and columns to show where things are located!
• Horizontal axis (x-axis): Goes left to right
• Vertical axis (y-axis): Goes up and down
• Coordinates: Written as (x, y)
• Origin: The point (0, 0) where axes meet
Directions on Maps:
North ⬆️ - Up
South ⬇️ - Down
East ➡️ - Right
West ⬅️ - Left
📐 Find the Area of Rectangles and Squares
What is Area?
Area is the amount of space inside a 2D shape! It tells us how many square units fit inside.
Area is measured in square units like cm², m², or square inches.
Area of a Rectangle:
\(\text{Area} = \text{Length} \times \text{Width}\)
\(A = l \times w\)
Example:
A rectangle has length = 8 cm and width = 5 cm. Find the area.
Formula: \(A = l \times w\)
Substitute: \(A = 8 \times 5\)
Calculate: \(A = 40\)
Answer: 40 cm² ✓
Area of a Square:
\(\text{Area} = \text{Side} \times \text{Side}\)
\(A = s \times s = s^2\)
Example:
A square has side = 6 cm. Find the area.
Formula: \(A = s^2\)
Substitute: \(A = 6^2\)
Calculate: \(A = 6 \times 6 = 36\)
Answer: 36 cm² ✓
💡 Remember: Always write the answer in square units (cm², m², etc.)!
❓ Find the Missing Side Length of a Rectangle
How to Find Missing Side Length:
If you know the area and one side, you can find the missing side!
Formulas:
If you know Area and Length:
\(\text{Width} = \text{Area} \div \text{Length}\)
\(w = A \div l\)
If you know Area and Width:
\(\text{Length} = \text{Area} \div \text{Width}\)
\(l = A \div w\)
Examples:
Example 1: Find the Width
A rectangle has area = 48 cm² and length = 8 cm. Find the width.
Given: Area = 48 cm², Length = 8 cm
Formula: \(w = A \div l\)
Substitute: \(w = 48 \div 8\)
Calculate: \(w = 6\)
Answer: Width = 6 cm ✓
Example 2: Find the Length
A rectangle has area = 56 m² and width = 7 m. Find the length.
Given: Area = 56 m², Width = 7 m
Formula: \(l = A \div w\)
Substitute: \(l = 56 \div 7\)
Calculate: \(l = 8\)
Answer: Length = 8 m ✓
💡 Check Your Answer: Multiply length × width. You should get the area!
📝 Important Formulas Summary
2D Shapes:
Sides = Vertices = Angles
(For all polygons)
3D Shapes (Euler's Formula):
\(F + V = E + 2\)
(Faces + Vertices = Edges + 2)
Area Formulas:
Rectangle: \(A = l \times w\)
Square: \(A = s^2\)
Find Missing Side:
\(l = A \div w\) or \(w = A \div l\)
💡 Quick Learning Tips
- ✓ 2D shapes are flat (length and width only)
- ✓ 3D shapes are solid (length, width, and height)
- ✓ Polygons have straight sides and are closed
- ✓ Circles and ovals are NOT polygons (curved sides)
- ✓ For 2D shapes: Sides = Vertices = Angles
- ✓ For 3D shapes: F + V = E + 2 (Euler's Formula)
- ✓ Face = flat surface, Edge = line where faces meet, Vertex = corner
- ✓ Reflection = Flip, Rotation = Turn, Translation = Slide
- ✓ Line of symmetry divides a shape into two equal mirror halves
- ✓ Area of rectangle = length × width
- ✓ Area of square = side × side (s²)
- ✓ To find missing side: divide area by known side
- ✓ Always use square units for area (cm², m², etc.)
- ✓ A square is a special rectangle with all sides equal
- ✓ Practice identifying shapes in real life!