Basic Geometry, Symmetry, Perimeter and Area: Class 6 Study Guide
Geometry names the shapes around us and measures them.
A point marks a position. A line extends endlessly both ways, a ray starts at a point and goes on one way, and a line segment has two endpoints. Two lines in a plane that never meet are parallel; those that meet at 90° are perpendicular.
An angle is formed by two rays from a common point (the vertex). It is measured in degrees with a protractor. A polygon is a closed shape with straight sides; a triangle has 3 sides, a quadrilateral 4, a pentagon 5 and a hexagon 6.
Angles and triangles
| Angle | Measure | Triangle type | Rule |
|---|---|---|---|
| Acute | less than 90° | Equilateral | 3 equal sides, 60° each |
| Right | 90° | Isosceles | 2 equal sides |
| Obtuse | between 90° and 180° | Scalene | no equal sides |
| Straight | 180° | Right-angled | one 90° angle |
Symmetry
A figure has line symmetry if a line divides it into two mirror-image halves. A square has 4 lines of symmetry, a rectangle 2, an equilateral triangle 3 and a circle infinitely many. The letters A, H and M have a vertical line of symmetry. Rangoli and kolam designs are good examples of symmetry in Indian art.
In your mind or on paper.
Edges overlap exactly.
That is a line of symmetry.
Look for more.
Perimeter and area
The perimeter of a shape is the total length of its boundary. Rectangle: 2 × (l + b). Square: 4 × side. Triangle: the sum of the three sides. The area is the surface it covers, in square units. Rectangle: l × b. Square: side × side. A rectangular field 40 m by 25 m has a perimeter of 130 m and an area of 1000 m². To find the area of an L-shape, split it into rectangles and add.
Worked examples and common mistakes
Example: The angles of a triangle add up to 180°. If two angles are 50° and 70°, the third is 180° − 120° = 60°. Common mistakes: using cm for area instead of cm², mixing up perimeter and area and using a protractor from the wrong zero. Draw the figure and label it before you calculate.
Check your understanding: model answers
1. 50°. 2. Area 40 m²; perimeter 26 m. 3. Four.
✨ Key Takeaways
- Parallel lines never meet; perpendicular lines meet at 90°.
- Angles of a triangle add to 180°.
- Perimeter is distance around; area is surface covered.
- Symmetry means mirror halves.
💬 Questions for Discussion & Reflection
- Find the third angle of a triangle with 45° and 85°.
- Find the area and perimeter of a rectangle 8 m by 5 m.
- How many lines of symmetry does a square have?
Print graph paper for geometry →