Angles, Parallel Lines, Triangles and Area: Year 7 Study Guide
Geometry gives rules that let us calculate unknown angles and areas without measuring.
When a transversal crosses two parallel lines, equal angles form: corresponding angles are equal (F shape), alternate angles are equal (Z shape) and co-interior angles add to 180° (C shape). Vertical (opposite) angles are always equal, and angles on a straight line add to 180°.
The angles in a triangle add to 180°, and the angles in a quadrilateral add to 360°. Triangles are classified by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse).
Angle relationships
| Relationship | Rule | Shape clue |
|---|---|---|
| Corresponding | equal | F |
| Alternate | equal | Z |
| Co-interior | add to 180° | C |
| Vertically opposite | equal | X |
| Straight line | add to 180° | — |
| Around a point | add to 360° | — |
Area
Area of a rectangle = length × width. Parallelogram = base × perpendicular height. Triangle = ½ × base × height. Trapezium = ½ × (a + b) × h. For a composite shape, split it into simple shapes, find each area and add them (or subtract a missing part).
Mark known lengths.
For each part.
Include units.
Write the total in square units.
Solving angle problems
Give a reason for each step. Example: two lines are parallel, one angle is 65°; the alternate angle is also 65° and the co-interior angle is 180° − 65° = 115°. For a triangle with angles x, x + 20 and 40: 2x + 60 = 180, so x = 60. Set out working with the rule name beside each line, as is expected in tests.
Worked examples and common mistakes
Example: A triangle with base 12 cm and height 7 cm has an area of ½ × 12 × 7 = 42 cm². Common mistakes: using the slanted side instead of the perpendicular height, forgetting that co-interior angles add to 180° and giving an area in cm instead of cm². Check that each triangle's angles sum to 180°.
Check your understanding: model answers
1. 48°. 2. 30 cm². 3. 110°.
✨ Key Takeaways
- Alternate and corresponding angles are equal.
- Co-interior angles add to 180°.
- Triangle angles add to 180°.
- Triangle area = ½ × b × h.
💬 Questions for Discussion & Reflection
- Angles on a straight line: one is 132°. Find the other.
- Find the area of a triangle with base 10 cm and height 6 cm.
- Two parallel lines: a co-interior angle is 70°. Find the other.