Lines, angles, triangles and quadrilaterals
Lines and angles
- Two lines are parallel if they never meet, perpendicular if they meet at a right angle.
- Angles are named by size:
| Name | Size |
|---|---|
| acute | less than $90^{\circ}$ |
| right | exactly $90^{\circ}$ |
| obtuse | between $90^{\circ}$ and $180^{\circ}$ |
| reflex | between $180^{\circ}$ and $360^{\circ}$ |
- Name an angle with three letters: angle $ABC$ is the angle at $B$.
Practice
An angle of 40° is called:
Less than 90° is acute.
Triangles
- A triangle has three sides; its angles add up to $180^{\circ}$.
- equilateral: all sides equal, all angles $60^{\circ}$. isosceles: two sides and two angles equal. scalene: all different.
- Worked example: angles $x$, $2x$, $90^{\circ}$ → $3x + 90 = 180$ → $x = 30^{\circ}$.
Practice
A triangle has angles x, 2x and 90°. Find x (in degrees).
x + 2x + 90 = 180, so 3x = 90 and x = 30°.
Quadrilaterals
- A quadrilateral has four sides; its angles add up to $360^{\circ}$.
- square (4 equal sides, 4 right angles), rectangle, parallelogram (opposite sides parallel), rhombus (4 equal sides), kite (2 pairs of equal touching sides), trapezium (one pair of parallel sides).
Practice
The four angles of a quadrilateral add up to how many degrees?
A quadrilateral can be split into two triangles: 2 × 180 = 360°.
Practice
Match each quadrilateral to its property.
A square has 4 equal sides and 4 right angles; a trapezium has one parallel pair; a kite has two adjacent equal pairs.
You've got it
Key idea
- acute $<90^{\circ}$, right $=90^{\circ}$, obtuse $90$–$180^{\circ}$, reflex $180$–$360^{\circ}$
- triangle angles add to $180^{\circ}$; quadrilateral angles add to $360^{\circ}$
- name an angle by three letters — the middle letter is the corner