The ruler-and-compass constructions, checked the way a mark scheme checks them: by where the constructed line or point must be.
What you will learn
- Draw the perpendicular bisector of a line segment and know what it gives
- Bisect an angle
- Find the foot of the perpendicular from a point to a line (Higher)
- Construct a triangle from three sides and find its third corner
- Choose the construction a problem needs
What each construction gives
- Perpendicular bisector of AB: every point on it is the same distance from A and from B. It passes through the midpoint of AB at right angles.
- Angle bisector: every point on it is the same distance from the two arms of the angle.
- Perpendicular from a point to a line: the shortest distance from the point to the line.
- Triangle from three sides: arcs of the two other lengths from the ends of the base cross at the third corner. For AB = 8 cm, AC = 6 cm and BC = 7 cm, draw AB, then an arc of radius 6 cm centred on A and an arc of radius 7 cm centred on B: they cross at C. Each arc is centred on the end that its side comes from.
- Angles: 60° from an equilateral triangle, 90° from a perpendicular; bisect them for 30° and 45°.
On a paper, leave the arcs showing: they earn the method marks. A mark scheme then checks the result with a ruler, within about 2 mm.
The rest of this lesson and its 11 practice questions are locked.
In this lesson
- What each construction gives
- Checking on a grid
- Equations of perpendicular lines (Higher)
- Coordinates from lengths
11 practice questions, marked as you go; about 25 minutes in all.
Key terms
Vertex, Vertices, Negative reciprocal
In this unit: Drawing and constructing
The answers papers ask you to draw: graphs plotted from a table, sketches with their key points, statistical charts, ruler-and-compass constructions and loci, each checked the way a mark scheme checks it.
- Plotting graphs
- Sketching graphs
- Drawing charts
- Constructions on a grid
- Loci and bearings