Lines & Angles
A point shows an exact location. It has no length, breadth or height. Shown by a fat dot & named with a capital letter — e.g. Point A.
The shortest path joining two points. Has 2 fixed end points. Written as AB or BA.
A line segment extended endlessly on both sides. No end points! Written as AB (with arrows) or a small letter like l, m.
A portion of a line that starts at one fixed point and goes on endlessly in one direction only. Written as DP (D = starting point).
⭐ Golden Rule: Only ONE line can pass through 2 fixed points, but infinite lines can pass through a single point!
Formed when two rays share the same starting point.
- Vertex → common starting point (B)
- Arms → the two rays (BD & BE)
- Naming → ∠DBE or ∠EBD (vertex always in middle)
- Symbol used: ∠
🌀 Size of an angle = amount of rotation/turn needed to bring one arm onto the other — NOT about the length of the arms!
- Superimposition: place one angle over another — vertices must overlap. Whichever opens wider is greater.
- Equal angles: when vertex + both arms overlap exactly after superimposing.
- Without superimposing: use a transparent circle — mark points where arms cut the circle, then compare on same circle.
❗ Note: Length of the arms drawn does NOT change the angle's size — only the amount of turning matters!
A full circle (1 full turn) = 360°. It is divided into 360 equal parts; each part = 1 degree (1°).
360°
(Straight ∠)
180°
(Right ∠)
90°
A protractor = half-circle divided into 180 equal 1° parts
📌 Steps to measure: place centre of protractor on the vertex → align one arm with 0° line → read where the other arm crosses the scale (use inner/outer scale correctly!).
A ray that divides an angle into two EQUAL halves. Found practically by paper folding so one arm overlaps the other.
| Type | Degree Range | Looks Like |
|---|---|---|
| Acute | 0° < ∠ < 90° | 🔺 sharp / narrow |
| Right | exactly 90° | ◻️ like an 'L' |
| Obtuse | 90° < ∠ < 180° | 📐 wide / blunt |
| Straight | exactly 180° | ➖ a straight line |
| Reflex | 180° < ∠ < 360° | 🌙 the "bigger" outside angle |
🧠 Remember: Acute = sharp, Obtuse = blunt. Two right angles (90°+90°) make one straight angle (180°)!
📎 Two lines meeting at 90° are called perpendicular lines.
✅ Quick Revision Checklist
- I can define point, line segment, line & ray with correct notation
- I know an angle = 2 rays + common vertex, and how to name it correctly
- I understand angle size = amount of rotation, not arm length
- I can compare angles using superimposition
- I know 1 full turn = 360°, half turn = 180°, quarter turn = 90°
- I can use a protractor correctly (0° line + right scale)
- I can classify angles: acute / right / obtuse / straight / reflex
- I know what an angle bisector is