Geometry (Sec 2) Practice
Apply Pythagoras' Theorem, congruence tests (SSS, SAS, AAS, RHS), similarity, interior and exterior angle properties of polygons, and geometric proof. These skills recur throughout the O-Level paper.
Common Mistakes to Avoid
Using Pythagoras on non-right-angled triangles
Confusing congruence (same size and shape) with similarity (same shape, different size)
Incorrectly summing interior angles: (n − 2) × 180° applies to any polygon, not just regular ones
Practice Questions
Try each question. When you're stuck, reveal the Socratic strategy — a guided hint that teaches you how to think, not just what to write.
A right-angled triangle has legs of 5 cm and 12 cm. Find the hypotenuse.
Find the sum of the interior angles of a regular hexagon.
Two triangles ABC and DEF have AB = DE, BC = EF, and angle B = angle E. Are they congruent? State the congruence test.
Parent & Tutor Insight
Geometry proofs are intimidating but highly structured. Teach your child to always state a reason for every step ('angles on a straight line', 'corresponding angles, AB ∥ CD'). Examiners award marks for reasons, not just calculations.
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Common Questions
What are the four congruence tests and how do I remember them?
SSS (Side-Side-Side): all 3 sides equal. SAS (Side-Angle-Side): 2 sides and the included angle equal. AAS (Angle-Angle-Side): 2 angles and a corresponding side equal. RHS (Right angle-Hypotenuse-Side): for right-angled triangles. Note: AAA is NOT a congruence test (only similarity).
What is the difference between congruence and similarity?
Congruent triangles are identical — same shape, same size, all sides and angles equal. Similar triangles have the same shape (angles are equal) but different sizes (sides are in proportion). Congruence is a special case of similarity with a scale factor of 1.
When can I use Pythagoras' Theorem?
Only in right-angled triangles. Pythagoras relates the three sides: a² + b² = c², where c is the hypotenuse (the side opposite the right angle). If there is no right angle, you need trigonometry (introduced in Sec 3).