Geometry : SGT
Geometry
Basic Geometrical Ideas
| Term | Meaning | Example |
|---|---|---|
| Point | Exact position, no size | Tip of a needle |
| Line | Extends endlessly in both directions | Railway track line |
| Line Segment | Part of a line with two endpoints | Edge of a book |
| Ray | Starts at one point, goes infinitely one side | Sun ray |
| Curve | Bent line | Circle boundary |
| Polygon | Closed figure with straight sides | Triangle, square |
| Angle | Formed by two rays from a point | Corner of a table |
Point has no length, width or thickness – only position.
A polygon must be closed and made only with straight lines.
Understanding Lines and Angles
| Concept | Description |
|---|---|
| Parallel Lines | Never meet, remain same distance apart |
| Intersecting Lines | Meet at a point |
| Transversal | Line cutting two other lines |
| Adjacent Angles | Angles sharing a common arm |
| Vertically Opposite Angles | Formed by intersecting lines, equal in measure |
| Type of Angle | Measure |
|---|---|
| Acute | Less than 90° |
| Right | 90° |
| Obtuse | 90° to 180° |
| Straight | 180° |
| Reflex | More than 180° |
Vertically opposite angles are always equal.
Sum of angles on a straight line = 180°.
Basic 2D Shapes and Naming
| Shape | Sides | Vertices |
|---|---|---|
| Triangle | 3 | 3 |
| Square | 4 equal | 4 |
| Rectangle | 4 | 4 |
Naming of any figure is done using its corner points in order.
Always move clockwise while naming vertices of a figure.
Triangles
| Type | Property |
|---|---|
| Equilateral | All sides equal |
| Isosceles | Two sides equal |
| Scalene | All sides unequal |
| Right-angled | One angle is 90° |
| Congruence Rule | Meaning |
|---|---|
| SSS | All sides equal |
| SAS | Two sides and included angle equal |
| ASA | Two angles and side equal |
| RHS | Right angle, hypotenuse and side |
Sum of angles of a triangle is always 180°.
Congruent triangles have same shape and same size.
Polygons and Quadrilaterals
| Quadrilateral | Property |
|---|---|
| Parallelogram | Opposite sides equal and parallel |
| Rectangle | All angles 90° |
| Square | All sides equal and angles 90° |
| Rhombus | All sides equal |
| Kite | Two pairs of adjacent equal sides |
| Trapezium | One pair of parallel sides |
Sum of all interior angles of quadrilateral = 360°.
Diagonal of a square bisects each other at right angles.
Three-Dimensional Shapes
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Cone | 2 | 1 | 1 |
| Cylinder | 3 | 2 |