Construction of Basic Geometric Figures (Bisecting Lines and Angles)
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Lesson overview
The geometric construction methods for bisecting a line and an angle.
Go to lesson quiz →Exam guidance · WAEC WASSCE Paper 1 + Paper 2 Lens
Pacing
Objective speed on Paper 1 + structured step-by-step method marks on Paper 2 Theory/Practical.
How WAEC marks this
Examiners award method marks (M1) for stating the formula/definition and accuracy marks (A1) ONLY when SI units are written.
Watch out for
Writing bare numbers without working or omitting SI units loses up to 50% of Paper 2 marks even when the final value is right.
Lesson content
Overview — Construction of Basic Geometric Figures (Bisecting Lines and Angles)
The geometric construction methods for bisecting a line and an angle. This lesson is at the beginner level — by the end, you'll be able to recognise this question type, apply a reliable method, and avoid the traps that cost marks.
Key Concept
Bisecting a line means dividing it into two exactly equal parts; bisecting an angle means dividing it into two exactly equal angles — both achieved through compass-and-straightedge construction methods that guarantee mathematical accuracy, rather than estimation.
Why It's Tested This Way
WAEC tests bisection methods because they are foundational construction techniques used repeatedly within more complex technical drawings, and precise, correct compass construction (not measurement by eye) is what the examiner checks for.
Method
When answering, follow the precise construction sequence step by step: for bisecting a line, draw intersecting arcs of equal radius from each endpoint above and below the line, then join the two intersection points; for bisecting an angle, draw an arc crossing both arms, then two further equal arcs from those crossing points to find the bisector.
Worked Example
Worked example: To bisect a straight line AB, set a compass to any radius greater than half of AB's length, draw arcs from both A and B that intersect above and below the line, then draw a straight line through both intersection points — this line crosses AB at its exact midpoint, perpendicular to it.
Second Worked Example
Second worked example: To bisect an angle at vertex O, draw an arc of any radius centred at O crossing both arms of the angle, then from each of those two crossing points, draw equal-radius arcs that intersect each other; a line from O through that new intersection point bisects the original angle exactly.
Common Traps
Common trap: attempting to bisect a line or angle by simply measuring with a ruler or protractor and marking the midpoint or half-angle — WAEC specifically tests the correct COMPASS CONSTRUCTION method, since the subject values demonstrated geometric construction technique over a measured approximation.
Lesson Summary
Remember: (1) identify what is being asked, (2) apply the WAEC strategy, (3) check against the traps. Complete the 10-question quiz below to unlock the next lesson — you need at least 60% to pass.
Mastery Check · Lesson Quiz · pass 60%
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