Geometry — Shapes, Lines, and Tangrams
1. Basic Geometric Ideas
Point:
A POINT is an EXACT location. It has NO size.
'We show a point with a DOT and name it with a letter: ● A'
Line:
A LINE is a straight path that goes on FOREVER in both directions.
Line Segment:
A LINE SEGMENT is a part of a line with TWO endpoints.
'You can MEASURE a line segment with a ruler.'
Ray:
A RAY has ONE endpoint and goes on FOREVER in ONE direction.
'The SUN'S rays start at the sun (endpoint) and travel in one direction!'
| Term | Endpoints | Picture |
|---|---|---|
| Point | None | ● |
| Line | None (goes forever both ways) | ⟷ |
| Line Segment | Two | ●—● |
| Ray | One | ●—⟶ |
2. 2D Shapes (Flat Shapes)
Two-dimensional shapes have LENGTH and WIDTH but NO thickness.
Circle:
- A CLOSED curve with all points the SAME distance from the centre.
- NO corners. NO sides.
'The wheel of a bicycle is a CIRCLE. A coin is a CIRCLE.'
Square:
- 4 EQUAL sides.
- 4 corners (right angles).
- All sides are the SAME length.
'A chess board is made of SQUARES. A Rubik's Cube has square faces.'
Rectangle:
- 4 sides — OPPOSITE sides are EQUAL.
- 4 corners (right angles).
'A DOOR is a rectangle. A BOOK is a rectangle.'
Triangle:
- 3 sides and 3 corners.
- Can be different shapes — some with equal sides, some with different sides.
'A pizza slice looks like a TRIANGLE. A sandwich cut diagonally makes triangles.'
| Shape | Number of Sides | Number of Corners |
|---|---|---|
| Circle | 0 (curved) | 0 |
| Square | 4 (equal) | 4 |
| Rectangle | 4 (opposite equal) | 4 |
| Triangle | 3 | 3 |
3. 3D Shapes (Solid Shapes)
Three-dimensional shapes have LENGTH, WIDTH, and DEPTH (or height).
Cube:
- 6 square faces (ALL equal).
- 12 edges.
- 8 corners (vertices).
- 'A DICE is a cube. A SUGAR CUBE is a cube.'
Cuboid:
- 6 rectangular faces (opposite faces equal).
- 12 edges.
- 8 corners.
- 'A BRICK is a cuboid. A BOOK is a cuboid.'
Sphere:
- 1 curved surface.
- NO edges. NO corners.
- 'A BALL is a sphere. A GLOBE is a sphere.'
Cylinder:
- 2 flat circular faces (top and bottom).
- 1 curved surface.
- 'A COLD DRINK CAN is a cylinder. A CANDLE is a cylinder.'
Cone:
- 1 flat circular face (base).
- 1 curved surface.
- 1 point (vertex) at the top.
- 'An ICE CREAM CONE is a cone. A PARTY HAT is a cone.'
| Solid Shape | Faces | Corners | Edges |
|---|---|---|---|
| Cube | 6 squares | 8 | 12 |
| Cuboid | 6 rectangles | 8 | 12 |
| Sphere | 1 curved | 0 | 0 |
| Cylinder | 2 circles + 1 curved | 0 | 2 |
| Cone | 1 circle + 1 curved | 1 | 1 |
4. Tangrams
A TANGRAM is an ancient Chinese puzzle made of 7 pieces (called TANS).
'The 7 tans are: 5 triangles (2 large, 1 medium, 2 small), 1 square, and 1 parallelogram.'
Rules of Tangram:
- Use ALL 7 pieces.
- Pieces must NOT overlap.
- Pieces can be ROTATED or FLIPPED.
Shapes You Can Make:
- Animals (cat, dog, bird, fish)
- People (running, dancing, sitting)
- Objects (house, boat, candle, letter)
- Numbers and letters
'Tangrams help you understand how shapes FIT TOGETHER. They are great for CREATIVE THINKING!'
Activity Idea:
Try making a SQUARE using ALL 7 tangram pieces. It is TRICKIER than it looks!
5. Common Mistakes
- Confusing 2D and 3D shapes: 'A square is FLAT (2D). A cube is SOLID (3D). They are DIFFERENT!'
- Calling a cuboid a cube: 'A cube has ALL equal sides. A cuboid has different lengths for length, width, and height.'
- Thinking a circle has sides: 'A circle has NO sides — it is a SINGLE CURVED line.'
- Confusing edges and faces: 'An EDGE is where TWO faces meet. A FACE is a FLAT surface. A cube has 6 faces and 12 edges.'
6. Key Facts to Remember
- 'A point has NO size — it is just a location.'
- '2D shapes are FLAT — circle, square, rectangle, triangle.'
- '3D shapes are SOLID — cube, cuboid, sphere, cylinder, cone.'
- 'A square has 4 EQUAL sides. A rectangle has OPPOSITE equal sides.'
- 'A sphere has NO edges and NO corners.'
- 'Tangrams use 7 pieces to make many shapes.'
7. Self-Test
Q1: Draw and name a shape with 4 equal sides and 4 corners.
Q2: How is a square different from a rectangle?
Q3: Name a 3D shape that has 6 square faces.
Q4: How many edges does a cube have?
Q5: Name a 3D shape with NO edges and NO corners.
Q6: What is the difference between a line and a line segment?
Q7: How many pieces does a tangram have?
Q8: What shape is a party hat?
Answers:
A1: A SQUARE (4 equal sides, 4 right-angle corners). A2: A square has ALL 4 sides equal. A rectangle has OPPOSITE sides equal. A3: A CUBE. A4: 12 edges. A5: A SPHERE (like a ball). A6: A line goes on forever in BOTH directions. A line segment has TWO endpoints and can be measured. A7: 7 pieces (5 triangles, 1 square, 1 parallelogram). A8: A CONE.
