GCSE · Maths · AQA · Spec 8300
Geometric terms and notation
Turn a triangle upside down, stretch it, flip it. ∠ABC is still the same angle, because in geometry a name is an address, not a description of the picture.
Triangle ABC
The names follow the vertices
∠ABC is the angle at B, the middle letter (∠CBA names the same angle). Side a is BC, the side opposite A; side b is CA, opposite B; side c is AB, opposite C.
Drag A or C left and right, or drag B up and down. Each time you move one vertex, watch the three side readouts: exactly one of them never changes. It is always the side the moving vertex does not touch, and it carries that vertex's letter in lower case.
The words behind the letters
Say the definition to yourself before you turn each card.
Parallel and perpendicular
Marks, not looks
What does each diagram actually prove about the pair of lines? Sort by the marks and statements, not by how the lines look.
Still to sort
Shown parallel (0)
Matching arrowheads, or the symbol ∥
Where the line is: The arrowheads must match: one > with one >, or >> with >>.
Shown perpendicular (0)
A small square where they meet, a stated 90°, or the symbol ⊥
Where the line is: The square is drawn in the corner where the two lines meet; it means the angle there is exactly 90°.
Not shown either way (0)
No mark and no statement, so you cannot say
Where the line is: Looking parallel or looking square is not evidence. Without a mark or a statement, it is not known.
Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle (90°).
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
A few letters and marks say exactly which point, side or angle you mean, however the figure is drawn.
What you need to know
- A point is named with a capital letter, and a line segment by its two end points, such as AB.
- An angle is named with three letters, and the middle letter is the vertex: ∠ABC (or ∠CBA) is the angle at B.
- In triangle ABC, the side opposite vertex A is labelled a, the side opposite B is b, and the side opposite C is c.
- Matching arrowheads show parallel lines (∥); a small square shows a right angle, so the lines meeting there are perpendicular (⊥).
- A regular polygon has all sides equal and all angles equal. A polygon may have line symmetry, rotation symmetry, both or neither.
The big picture
Geometry has its own written language. Points are named with capital letters, a line segment by its two end points, and an angle by three letters with the vertex in the middle, so ∠ABC is the angle at B. In triangle ABC, side a is opposite vertex A, side b is opposite B and side c is opposite C. On a diagram, matching arrowheads show parallel lines and a small square shows a right angle; without a mark or a statement, you cannot assume either. A polygon is regular when all its sides and all its angles are equal, and polygons can have line symmetry, rotation symmetry, both or neither.
Key points
Worked example
Problem
Sketch quadrilateral ABCD from this description: AB ∥ DC, AD ⊥ DC, AB = 4 cm and DC = 7 cm.
⚠ Watch out
Reading an angle's name from its first letter. ∠XYZ is the angle at Y, not at X, because the vertex is always the middle letter. The same slip happens with sides: side x is YZ, the side opposite X, not a side that runs into X.
Memory hook
Middle for the corner, opposite for the side, marks not looks.
Check yourself
A sketch of EFGH has one arrowhead on EF, one on HG, and a small square at H. What do these marks say in notation? Check: EF ∥ HG and ∠EHG = 90°.
Flashcards
(12)How is a point named?
What is the difference between a line and a line segment?
What is a vertex?
What is an edge of a solid?
What is a plane?
Which angle does ∠PQR name?
In triangle PQR, which side is labelled q?
What do parallel lines look like on a diagram, and what symbol is used?
How is a right angle shown on a diagram, and what does ⊥ mean?
What is a polygon?
What makes a polygon regular?
What is the order of rotation symmetry?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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