Perpendicular bisector and midpoint
Two arcs of the same radius from A and from B cross on both sides of the segment: the line through the crossings is the perpendicular bisector. Level 3 divides the segment into four parts.
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Teaching guide: compass and ruler constructions in Grades 6 to 8
Constructing a perpendicular bisector, an angle bisector or a parallel line with a compass is the base of geometric drawing taught from Grade 6 to Grade 8 (Years 7 to 9). This free geometric constructions worksheet generator builds A4 worksheets with the data drawn to true size, the room each construction needs and a measurement to check it, with an answer key that draws every arc.
- For
- Elementary 6th · Middle & High 7th, 8th (ages 11-13)
- Subject
- Mathematics › Geometry & Measurement
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Angle bisector
An arc from the vertex cuts both arms; two equal arcs from those points mark the bisector. Each half is checked with a protractor.
Perpendicular and parallel lines
The perpendicular from a point on the line or off it, with its foot H and the distance, and the parallel by the rhombus method. Level 3 builds a square and a parallelogram.
Copying angles
Copying an angle onto a ray with a compass, and adding two angles by placing one next to the other.
Constructing triangles
From three sides (SSS), two sides and the included angle (SAS) or a side and two angles (ASA). The sides are drawn to true size to take with the compass.
Centres and polygons
The circumcentre, incentre and centroid with their circles, and regular polygons inscribed in a circle: from the hexagon and the square to the pentagon.
Frequently asked questions about the geometric constructions worksheets
Which grades are these worksheets for?
Grades 6 to 8 (Years 7 to 9). Perpendicular bisectors, angle bisectors, perpendicular and parallel lines start in Grade 6; copying angles, constructing triangles and inscribed polygons in Grade 7, and the centres of a triangle in Grade 8.
Is the data printed to true size?
Yes. Segments, angles and circles are drawn with the measurements of the answer key. Print at 100 % (turn off "fit to page") and check with the 5 cm line at the top of the sheet.
Why does each construction ask for a measurement?
The measurement checks the construction: if the perpendicular bisector is right, AM is half the segment; if the triangle is right, the missing angle or side matches the answer key. Being 1 mm or 1 degree out is normal.
Which methods does the answer key use?
The usual compass and ruler methods: arcs from both ends for a perpendicular bisector, arcs from the arms for an angle bisector, a rhombus for a parallel, the midpoint of a radius for the pentagon. Arcs and construction lines are drawn in blue.
Do pupils need a protractor or a set square?
Constructions are made with a ruler and a compass. The protractor is only used to measure the angles of the result and to draw the angles of the triangles given in degrees.
Is there enough room to construct?
Every exercise has the room the answer key's construction takes, with a margin for the arcs, and the data is placed so that the arcs fit.
What other worksheets go well with these?
The angles worksheets to measure and draw with a protractor, the symmetry worksheets and Pythagoras' theorem. Find every resource under maths worksheets.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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