Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Measuring Line Segments
A ruler (scale) is used to measure line segments. The unit is centimetres (cm) or millimetres (mm).
- Place the ruler so that the 0 mark aligns with one end.
- Read the mark at the other end.
Comparing lengths:
- Direct comparison: place side by side.
- Using a ruler: measure and compare the numbers.
- Using a compass: transfer lengths for comparison.
Types of Angles
An angle is measured in degrees (°) using a protractor.
| Type | Measure | Example |
|---|---|---|
| Zero angle | 0° | Completely closed |
| Acute angle | Between 0° and 90° | 45°, 60° |
| Right angle | Exactly 90° | Corner of a page |
| Obtuse angle | Between 90° and 180° | 120°, 150° |
| Straight angle | Exactly 180° | A straight line |
| Reflex angle | Between 180° and 360° | 270° |
| Complete angle | Exactly 360° | Full turn |
Memory tip: 0° → Acute → 90° → Obtuse → 180° → Reflex → 360°
Perpendicular Lines
Two lines that meet at a right angle (90°) are perpendicular to each other.
- Denoted: AB ⊥ CD
- A perpendicular bisector is a line perpendicular to a segment passing through its midpoint.
Types of Triangles
Based on Sides
| Type | Property |
|---|---|
| Equilateral | All 3 sides equal; all angles = 60° |
| Isosceles | 2 sides equal; base angles equal |
| Scalene | All 3 sides different; all angles different |
Based on Angles
| Type | Property |
|---|---|
| Acute-angled | All 3 angles < 90° |
| Right-angled | One angle = 90° |
| Obtuse-angled | One angle > 90° |
Types of Quadrilaterals
| Shape | Properties |
|---|---|
| Square | All sides equal, all angles 90° |
| Rectangle | Opposite sides equal, all angles 90° |
| Rhombus | All sides equal, opposite angles equal |
| Parallelogram | Opposite sides parallel and equal |
| Trapezium | Exactly one pair of parallel sides |
Polygons
| Polygon | Sides | Interior angle (regular) |
|---|---|---|
| Triangle | 3 | 60° |
| Quadrilateral | 4 | 90° |
| Pentagon | 5 | 108° |
| Hexagon | 6 | 120° |
| Heptagon | 7 | — |
| Octagon | 8 | 135° |
Regular polygon: all sides equal AND all angles equal.
Three-Dimensional Shapes
3D shapes have length, breadth (width), and height.
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid (box) | 6 | 12 | 8 |
| Cylinder | 3 (2 circles + 1 curved) | 2 | 0 |
| Cone | 2 (1 circle + 1 curved) | 1 | 1 |
| Sphere | 1 curved | 0 | 0 |
| Triangular prism | 5 | 9 | 6 |
| Square pyramid | 5 | 8 | 5 |
Euler's formula: Faces + Vertices − Edges = 2
Key Vocabulary
| Term | Meaning |
|---|---|
| Acute angle | Less than 90° |
| Obtuse angle | Between 90° and 180° |
| Reflex angle | Between 180° and 360° |
| Equilateral | All sides equal |
| Isosceles | Two sides equal |
| Scalene | All sides unequal |
| Regular polygon | All sides and angles equal |
| Face | Flat surface of a 3D shape |
| Edge | Line where two faces meet |
| Vertex | Corner of a 3D shape |
Exam Tips
- Reflex angle is between 180° and 360° — students often forget this type.
- Equilateral triangle: all angles = 60° — useful fact for calculations.
- Euler's formula: F + V − E = 2 — used to verify or find missing values for 3D shapes.
- A square is a special rectangle (and also a special rhombus) — know the hierarchy.
- A protractor is used to measure angles — remember it measures from 0° to 180°.
- Right angle symbol is a small square drawn at the vertex.
Frequently Asked Questions
Acute angle: less than 90°. Right angle: exactly 90°. Obtuse angle: between 90° and 180°. Straight angle: exactly 180°. Reflex angle: between 180° and 360°. Complete angle: exactly 360°.