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GEOMETRIC CONSTRUCTION SKILLS
Introduction
In this topic you will learn how to construct lines, angles and geometric figures. Skills developed from this topic can be applied in day-to-day life.
Parallel ,Perpendicular and Intersecting lines
Exercise
Identify the lines below
Construction of Perpendicular Lines
Construction of parallel lines
Construction of special angles
1. In construction, of angles, we use a ruler, pencil and pair of compasses only.
Exercise
Activity : Sketching and Describing Loci
Sketch and describe what happens about the following:
1. A mark on the floor as the door opens and closes.
2. The centre of a bicycle wheel as the bicycle travels along a straight line.
3. A man is walking and keeping the same distance from two trees P and Q.
4. A student is walking in the class keeping the same distance from two opposite walls.
Relating Lines and Angles to Loci
locus is a set of points which satisfies a certain condition.
Activity : Demonstration of some simple Loci
Demonstrate how one can walk the same distance from a given point.
How one can walk the same distance from two fixed points.
How one can walk the same distance from a line.
How one can walk the same distance from two intersecting lines
Construction of Loci
Activity : Construction of a locus at a point equidistant from a fixed point.
The locus of points that are at a constant distance from a fixed point is a circle with radius equals to constant distance.
EXAMPLE
Construct the locus of a point Q at a constant distance of 2 cm from a fixed point P.
Activity : Construction of a locus of a point equidistant from a given line.
The locus of points that are at a constant distance from a straight line is a pair of parallel lines at a constant distance from the given straight line.
EXAMPLE
Construct the locus of a point P that moves a constant distance of 2 cm from a straight line AB
NOTE:
The locus of points at a fixed distance, d, from the point, P is a circle with the given point P as its center and d as its radius. i.e Given a fixed point, the locus of points is a circle.
The locus of the points at a fixed distance, d, from a line with end points AB, is a pair of parallel lines at a distance, d(apart) from AB and on either side of AB. i.e Given a straight line, the locus of points is two parallel lines.
The locus of points equidistant from two given points, A and B, is the perpendicular bisector of the line segment that joins the two points. i.e Given two points, the locus of points is a straight line midway between the two points.
The locus of points equidistant from two intersecting lines, L1 and L2, is a pair of bisectors that bisect the angles formed by line L1 and L2. i.e Given two intersecting lines, the locus of points is a pair of lines that cut the intersecting lines in half.
Exercise
1. Construct the locus of a point Q that moves a constant distance of 3 cm from a straight line XY
2. A dog is on a lead tethered to a post in the corner of a garden. The lead is 5 cm long. Describe the locus of the dog with a sketch.
3. Construct the locus of a point equidistant from two intersecting lines.
Construction of Geometric Figure
Construction of figures is an application of the locus, since during inscribing and circumscribing we use the knowledge of angle bisector.
Activity : Construction of geometrical figures.
Steps for circumscribing a circle on a triangle.
Construct the perpendicular bisector of one side of triangle.
Construct the perpendicular bisector of another side .
Where they cross is the center of the Circumscribed circle.
Place the compass on the center point, adjust its length to reach any vertex of the triangle, and draw your Circumscribed circle
EXAMPLE
Steps for inscribing a circle in a triangle.
Bisect two angles of a triangle
The angle bisector will intersect at the incenter(centre point)
Construct a perpendicular from the centre point to one side of the triangle..
Place the compass at the centre point and adjust its length up to where the perpendicular crosses the triangle, and then draw the inscribed circle.
EXAMPLE
Exercise
Situation of Integration
In a village, there is an old man who wants to construct a rectangular small house of wattle and mud.
Support: A string, sticks, panga, tape measure and human resource.
Resources: Knowledge of horizontal and vertical lines i.e. rows and columns, knowledge of construction of geometric figures.
Task: The community asks you to accurately construct the foundation plan for this old man’s house. Explain to the class how you have accurately constructed the foundation plan. Discuss whether there are other ways of constructing an accurate foundation plan.
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