Junior Cycle Constructions
Use a compass and straight edge to complete each construction below.
Each task includes an interactive Polypad and an optional video example.
- Bisector of a given angle.
- Perpendicular bisector of a line segment.
- Perpendicular to a given line through a point not on it.
- Perpendicular to a given line through a point on it.
- Parallel to a given line through a given point.
- Divide a segment into 2 or 3 equal parts.
- Divide a segment into \(n\) equal parts.
- Mark a line segment of given length on a ray.
- Construct an angle of a given measure.
- Triangle (SSS).
- Triangle (SAS).
- Triangle (ASA).
- Right triangle (hypotenuse and one side). RHS
- Right triangle (one side and acute angle). RSA
- Rectangle, given side lengths.
1. Angle Bisector
Construct the bisector of angle \(ABC\).
2. Perpendicular Bisector
Construct the perpendicular bisector of \([AB]\).
3. Perpendicular Through a Point (Not on Line)
Construct a line perpendicular to a given line \(\ell\), through a point \(P\) not on \(\ell\).
4. Perpendicular Through a Point on the Line
Construct a line perpendicular to a given line \(\ell\), through a point \(P\) on \(\ell\).
5. Parallel Line Through a Point
Construct a line parallel to AB, through a point \(P\).
6. Divide a Segment into 2 or 3 Equal Parts
Divide the line segment \([AB]\) into 3 equal parts.
7. Divide a Segment into n Equal Parts
Divide the line segment \([AB]\) into 5 equal parts.
8. Marking Off Lengths on a Ray
Mark off 3 lengths of 5cm length along a ray.
9. Constructing a Given Angle
Construct an angle of \(50^\circ\) with a given ray as one arm.
10. SSS Triangle Construction
Construct a triangle with side lengths \(8\text{ cm}, 12\text{ cm}\) and \(7\text{ cm}\) (SSS).
11. SAS Triangle Construction
Construct a triangle with sides \(10\text{ cm}\) and \(9\text{ cm}\) and included angle \(50^\circ\) (SAS).
12. ASA Triangle Construction
Construct a trianle with angles \(30^\circ\) and \(50^\circ\) adjacent to side of \(10\text{ cm}\) (ASA).
13. Right Triangle (RHS)
Construct a right-angled triangle, given the hypotenuse \(10\text{ cm}\) and one other side \(8\text{ cm}\) (RHS).
14. Right Triangle (RSA)
Construct a right-angled triangle, with a side of \(6\text{ cm}\) opposite an angle of \(40^\circ\) (RSA).
15. Rectangle Construction
Construct a rectangle with side lengths \(10\text{ cm}\) and \(6\text{ cm}\).
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