C5.1; E5.1 - Geometrical language

Lines and angles

Geometrical words describe exact features: turning a diagram does not change those features. A square balanced on a corner still has four right angles, so it is still a square.

Letters identify positions. The segment $AB$ joins points $A$ and $B$. Two lines are parallel if they lie in the same flat surface and never meet, however far extended. Matching arrow marks on the lines show that they are parallel. Different parallel pairs use different arrow marks.

Two lines are perpendicular if they meet at a right angle, $90^\circ$. A small square marks a right angle. Perpendicular lines can be sloping: “vertical” and “horizontal” describe directions on a page, whereas “perpendicular” describes the angle between two lines.

[DIAGRAM: asset_name: Line and angle vocabulary; asset_slug: lines_angle_vocabulary; caption: Matching arrows show parallel lines, a square shows a right angle, and an arc selects the angle being described.; description: Three exact panels show two sloping parallel lines with matching arrows, two perpendicular sloping lines with a right-angle square, and a polygon vertex with an interior angle and the adjacent exterior angle marked on an extended side.]

An angle measures a turn between two rays meeting at a vertex. One complete turn is $360^\circ$. The marked arc tells you which turn is meant.

For example, $38^\circ$ is acute, $126^\circ$ is obtuse and $244^\circ$ is reflex. A turn of $180^\circ$ is straight, not obtuse. The same two rays can enclose a smaller angle and a reflex angle, so attend to the arc.

An interior angle is inside a polygon at a vertex. An exterior angle is formed between a side and the extension of an adjacent side. Extend the actual side; an arbitrary angle outside a shape need not be its exterior angle.

A bearing gives the direction of one point from another. It is measured clockwise from north and written with three figures: due east has bearing $090^\circ$. North, east, south and west are the compass directions. You will use this vocabulary to measure and calculate bearings in the bearings lesson.

Use angle size and the marked turn, rather than the tilt of the picture.

Triangles and quadrilaterals

Count sides first, then use equality and angle properties to give a more precise name. Tick marks on sides mean equal lengths; matching arcs at vertices mean equal angles. A drawing's apparent lengths alone do not establish equality.

A triangle can have both a side description and an angle description. A right-angled triangle with two equal shorter sides is right-angled and isosceles; a right-angled triangle with all sides unequal is right-angled and scalene. “Right-angled” does not tell you whether two sides are equal.