Geometric Construction

Use ruler and compass to construct perpendicular bisectors, angle bisectors, 60°, 90°, 45°, 30°, and triangles.

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Curated Video Lesson

Visual explanation and practical step-by-step walk-through

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Comprehensive Study Notes

Aligned with Ghana NaCCA & WAEC BECE syllabus standards

Topic Introduction & Real-World Context:

Geometric construction is the precise drawing of lines, angles, and shapes using ONLY two instruments: an unmarked straight edge (ruler) and a pair of compasses. In the BECE exam, construction is a compulsory Section B question carrying 12 to 15 marks. Accuracy, clean arcs, and correct labeling are essential to secure maximum points.

What You Will Master in This Lesson (NaCCA Objectives):

Construct a perpendicular bisector of a line segment.

Bisect any given angle accurately using compasses.

Construct standard angles: 90°, 60°, 45°, 30°, and 15° using compasses only.

Construct a perpendicular to a line from a point on the line and from an external point.

Construct triangles given lengths of sides and sizes of angles.

1. Basic Construction Instruments & Rules

• Straight ruler: Used ONLY for drawing straight lines through points (not for guessing angles). • Pair of compasses: Used for drawing circles and intersecting arcs. Compasses must be tight and pencils sharp! • Golden WAEC Rule: NEVER erase construction arcs! Examiners mark the intersecting arcs to award method marks.

2. Perpendicular Bisector of a Line Segment

To bisect line segment AB: 1. Open compass to more than half the length of AB. 2. With center A, draw arcs above and below the line. 3. With center B and the SAME radius, draw arcs intersecting the first arcs at points P and Q. 4. Draw a straight line through P and Q. Line PQ bisects AB at 90°.

3. Constructing Standard Angles: 60°, 90°, 45°, 30°

• Angle of 60°: Draw a line segment. With center at vertex, draw an arc cutting the line. With the same radius and center at the cut point, draw an arc intersecting the first arc. Draw line through intersection = 60°. • Angle of 30°: Bisect the 60° angle. • Angle of 90°: Construct a perpendicular bisector or construct from a straight line (180° bisected). • Angle of 45°: Bisect the 90° angle.

Common Mistakes Students Make in BECE Examinations:

⚠️Erasing construction arcs. (This results in zero method marks!).

⚠️Using blunt pencils causing thick, inaccurate lines.

⚠️Changing the compass radius when drawing intersecting arcs from opposite ends.

Teacher's BECE Exam Pro-Tips:

⭐Keep pencil points needle-sharp.

⭐Draw light construction arcs and bold outline lines for the required triangle or figure.

⭐Measure lengths carefully using the millimeter markings on your ruler.

Quick Revision Summary Checklist:

Use only ruler and compass for standard angles.

Do not erase construction arcs.

Bisect 60° to get 30°; bisect 90° to get 45°.

Step-by-Step Worked Examples (1)

Real BECE exam-standard problems with complete solution steps

Example 1: Bisection of an Angle

Problem StatementDescribe the key steps to bisect a given angle ABC.

Step-by-Step Solution:

Step 1: With vertex B as center, draw an arc cutting arms BA and BC at points P and Q.

Step 2: With center P, draw an arc inside the angle space.

Step 3: With center Q and the SAME radius, draw an arc intersecting the first arc at point R.

Step 4: Draw a straight ray from vertex B through point R. Ray BR bisects angle ABC.

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Key Takeaway / Exam Rule: Always keep compass radius constant when drawing intersecting arcs from P and Q.

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