Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Accurately bisect any given line or angle.
• Construct parallel and perpendicular lines.
• Divide a line segment into a specified number of equal parts.
• Apply these constructions to solve simple problems.
• Demonstrate neatness and precision in all constructions.

Lesson summary

Engineering Graphics and Design (EGD) isn't just about drawing lines and shapes; it's about communicating ideas visually and accurately. Basic geometrical constructions are the foundation of this communication. These constructions are used in various fields from architecture and civil engineering to mechanical engineering and design. Think about building a house, designing a car, or even laying out a garden - geometric constructions are essential for accurate planning and execution.

Lesson notes

2.1 Bisecting a Line Segment: Bisecting a line means dividing it into two equal parts. The line that divides it is called the perpendicular bisector, because it also forms a right angle (90°) with the original line.

How to bisect a line segment AB: Place the compass point at A and open the compass to a radius greater than half the length of AB. Draw an arc above and below the line segment. Without changing the compass radius, place the compass point at B and draw arcs that intersect the arcs drawn in step

1. Label the points of intersection C and D. Draw a straight line through points C and D. The point where CD intersects AB is the midpoint of AB, and CD is the perpendicular bisector of A

B. Why this works: This construction relies on creating two congruent isosceles triangles (ACB and ADB). The line CD is the line of symmetry for the figure, ensuring it bisects AB at a right angle. 2.2 Bisecting an Angle: Bisecting an angle means dividing it into two equal angles.

How to bisect an angle BAC: Place the compass point at A (the vertex of the angle) and draw an arc that intersects both arms of the angle (AB and AC). Label the points of intersection D and E. Place the compass point at D and draw an arc inside the angle. Without changing the compass radius, place the compass point at E and draw an arc that intersects the arc drawn in step

2. Label the point of intersection

F. Draw a straight line from A to

F. The line AF is the angle bisector of angle BA

C. Why this works: This construction creates two congruent triangles (ADF and AEF) by side-side-side congruence (SSS). Since the triangles are congruent, their corresponding angles are equal, meaning angle BAF equals angle CAF. 2.3 Constructing Parallel Lines: Parallel lines are lines that never intersect, no matter how far they are extended.

Method 1: Using a Set Square and Ruler (T-square in a technical drawing environment) Place the ruler (or T-square) along the existing line (line L). Place the set square against the ruler. Slide the set square along the ruler to the desired position. The line you draw along the set square's edge will be parallel to line

L. Method 2: Constructing Equal Corresponding Angles Draw line L. Choose a point A outside of line L where you want the parallel line to pass through. Draw a transversal line from point A intersecting line L at point B. At point A, construct an angle equal to the angle formed by the transversal and line L at point B (corresponding angles). Extend the arm of the constructed angle from point

A. This line is parallel to line

L. Why these work: Method 1 relies on keeping the angle between the lines constant. Method 2 utilizes the theorem that if corresponding angles are equal, the lines are parallel. 2.4 Constructing Perpendicular Lines: Perpendicular lines intersect at a right angle (90°).

Method 1: From a Point ON a Line (using compass and straightedge) Let point P be on line L. With P as the center, draw an arc intersecting line L at two points, A and B. With A and B as centers, and a radius greater than AP (or BP), draw arcs that intersect each other. Label the intersection point

C. Draw a line through points C and

P. Line CP is perpendicular to line

L. Method 2: From a Point OFF a Line (using compass and straightedge) Let point P be outside line L. With P as the center, draw an arc that intersects line L at two points, A and B. With A and B as centers, and a radius greater than half the distance between A and B, draw arcs that intersect each other on the opposite side of line L from P. Label the intersection point

C. Draw a line through points P and

C. Line PC is perpendicular to line

L. Why these work: These methods leverage properties of circles and congruent triangles to create right angles. 2.5 Dividing a Line Segment into Equal Parts (Parallel Line Method): This method is particularly useful when you need to divide a line into a specific number of equal segments. How to divide a line segment AB into, say, 5 equal parts: Draw a line AC at any convenient angle to AB. Starting at A, use a compass to mark off 5 equal segments along AC (A1, A1A2, A2A3, A3A4, A4A5). The size of these segments is arbitrary; what matters is that they are all the same length. Join A5 to B. Using a set square and ruler (or T-square), draw lines parallel to A5B from A4, A3, A2, and A

1. These parallel lines will intersect AB, dividing it into 5 equal segments.

Why this works: This method relies on similar triangles and the properties of parallel lines. The parallel lines divide AC into equal segments, and because of the similarity of the triangles formed, they also divide AB into equal segments. Guided Practice (With Solutions)

Question 1: Bisect a line segment AB that is 80mm long.

Solution: Draw a line segment AB of 80mm length. Place the compass point at A and open the compass to a radius greater than 40mm (e.g., 50mm). Draw arcs above and below the line segment.