Basic geometry language, labelling and diagrams
Geometry and measures • Properties and constructions
Flashcards
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Key concepts
What you'll likely be quizzed about
Basic elements: points, lines, planes, vertices and edges
A point denotes a precise location and has no size; notation uses a single capital letter such as A or P. A line represents an infinite straight path in both directions and uses lowercase or two-point notation such as line AB or AB with an arrow sign. A plane denotes a flat two-dimensional surface that extends infinitely and uses a single script letter or three non-collinear points to name it. A vertex denotes the corner where two or more edges or lines meet; edges denote straight segments joining vertices in polygons and polyhedra. Clear naming prevents ambiguity when referring to specific locations or segments.
Parallel and perpendicular lines, and right angles
Parallel lines remain equidistant and never meet; notation uses the symbol ∥, for example AB ∥ CD. Perpendicular lines meet at a right angle; notation uses the symbol ⟂, for example AB ⟂ CD. A right angle measures exactly 90° and indicates perpendicularity. Cause → effect: perpendicular intersection causes a right angle; parallelism prevents intersection at any finite distance. Symbols and precise wording give direct information about angle size and intersection behaviour.
Polygons, regular polygons and symmetry
A polygon is a closed planar figure made from straight-line segments joined end to end. A regular polygon has all sides equal and all interior angles equal. Reflection symmetry occurs when a mirror line maps the polygon onto itself; rotation symmetry occurs when rotation about the centre by a certain angle maps the polygon onto itself. Limiting factors: symmetry statements require exact equality of specified sides or angles; visual similarity alone is insufficient to assert regularity or symmetry.
Labelling sides and angles of triangles
Standard notation labels triangle vertices with capital letters such as ABC. The side opposite vertex A is labelled a, opposite B is b, and opposite C is c; side notation uses lowercase letters corresponding to the opposite vertex. Angle at vertex A is written as ∠A or sometimes as A. Cause → effect: labelling sides by opposite vertices enables concise reference in formulae and proofs and prevents confusion when multiple triangles appear in a diagram.
Drawing diagrams from written descriptions
A diagram must reflect all given relationships and measurements without adding unproved information. Steps: identify named points and segments, mark parallel or perpendicular relations with standard symbols, place angle measures and lengths where specified, and check for consistency. Cause → effect: correct placement of symbols and labels ensures the diagram encodes the written constraints and supports accurate reasoning or calculation.
Perpendicular distance as the shortest distance to a line
The perpendicular from a point to a line meets the line at a right angle and yields the shortest possible segment connecting the point and the line. Cause → effect: any non-perpendicular segment from the point to the line is longer because it forms the hypotenuse of a right-angled triangle that has the perpendicular as a shorter leg. Limiting factor: the perpendicular must meet the given line (or its extension) at a right angle to qualify as the shortest distance.
Key notes
Important points to keep in mind