📐 Mastering Constructions: Triangles & Bisectors Made Easy!

Constructions lie at the heart of geometry—allowing us to create accurate diagrams *without* measurements beyond a straight-edge and compass. **Mastering these skills translates directly into easy marks in O Level exams** and strengthens spatial reasoning for higher-level topics.

Core Ideas & Must-Know Techniques

For Core level, focus on three pillars: **(1) constructing triangles from given information, (2) drawing angle and perpendicular bisectors, and (3) creating lines parallel or perpendicular to a given line**. Precision and logical order of steps are crucial, because examiners award marks for construction arcs and clear reasoning.

Use a sharp pencil and keep the compass width *fixed* until the intersection is marked.
Always label key points—examiners follow your labels when awarding method marks.

Worked Example: Constructing a Triangle from 3 Sides

Problem: Construct

\triangle ABC

where

AB = 5\,\text{cm}

BC = 6\,\text{cm}

and

AC = 7\,\text{cm}

. Show all construction lines.

Step 1: Draw base
$AB = 5\,\text{cm}$
with a straight-edge.
Step 2: With centre $A$ and radius
$7\,\text{cm}$
, draw an arc.
Step 3: With centre $B$ and radius
$6\,\text{cm}$
, draw another arc to intersect the first at $C$ .
Step 4: Join
$AC$
and
$BC$
to complete the triangle. Keep construction arcs faint but visible for method marks.

Practice makes perfect! **Re-draw each construction until the steps feel automatic** and you can finish within two minutes—exactly the speed needed under exam conditions.