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SingaporeMaths

Geometry and Properties of Circles

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What angle rules govern lines, triangles and polygons, and how do we use them?

Apply angle properties of parallel lines, triangles and polygons, including interior and exterior angle sums, to find unknown angles
A focused answer to the O-Level E-Maths outcome on angle properties. Angles on a line and at a point, parallel-line angles, the angle sum of a triangle, and interior and exterior angles of polygons.
8 min answer →

What angle relationships hold inside a circle, and how do tangents and chords behave?

Apply the circle theorems relating angles at the centre and circumference, angles in a semicircle and the same segment, cyclic quadrilaterals, and tangent properties
A focused answer to the O-Level E-Maths outcome on circle theorems. The angle at the centre, angle in a semicircle, angles in the same segment, cyclic quadrilaterals, and the tangent-radius and tangent properties.
10 min answer →

When are two figures congruent or similar, and how do scale factors work?

Identify congruent and similar figures, apply the conditions for congruence and similarity, and use scale factors for lengths, areas and volumes
A focused answer to the O-Level E-Maths outcome on congruence and similarity. The congruence conditions, the test for similar triangles, the linear scale factor, and the area and volume scale factors.
9 min answer →

How do we construct accurate figures and describe the set of points satisfying a condition?

Construct triangles, angle bisectors and perpendicular bisectors with compasses, and describe and draw simple loci
A focused answer to the O-Level E-Maths outcome on constructions and loci. Constructing perpendicular and angle bisectors, the standard loci, and combining conditions to find a region.
8 min answer →

How does Pythagoras theorem relate the sides of a right-angled triangle?

Apply Pythagoras theorem to find an unknown side in a right-angled triangle and to test whether a triangle is right-angled
A focused answer to the O-Level E-Maths outcome on Pythagoras theorem. The relationship between the hypotenuse and the other two sides, finding a missing side, the converse test, and applications.
7 min answer →