Plane Geometry

This topic covers the basic properties of angles, lines, triangles, quadrilaterals, polygons and circles. You will learn the angle rules needed for O-Level and how to apply them to find unknown angles.

  • Angles at a point and on a straight line
  • Parallel lines and transversals
  • Triangles and polygons
  • Circle theorems - basic facts

Lessons for Plane Geometry

Angle Facts: Points, Lines and Parallel Lines

Basic angle facts1. Angles at a point: Add up to 360°.2. Angles on a straight line: Add up to 180°.3. …

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Triangles and Polygons

TrianglesAngle sum: Angles in a triangle add to 180°.Exterior angle: Exterior angle = sum of two opposite interior angles.Isosceles triangle: …

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Quadrilaterals

Angle sumAngles in any quadrilateral add to 360°.Special quadrilateralsParallelogram: Opposite angles equal. Adjacent angles add to 180°. Opposite sides equal …

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Circle Theorems - Basic Facts

O-Level circle theorems1. Angle at centre: Angle at centre = 2 × angle at circumference, standing on the same arc.2. …

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Exercises for Plane Geometry

Find the missing angles

Find angle x in each case, giving a reason:Two angles on a straight line: 110° and xThree angles at a …

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Triangles and polygons

Calculate:A triangle has angles 50°, 60°. Find the third angle.In isosceles triangle ABC, AB=AC and ∠BAC = 40°. Find ∠ABC.Sum …

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Quadrilateral angles

Find angle x:Quadrilateral with angles 80°, 110°, 90°, xParallelogram with one angle 65°. Find the other three angles.Kite with angles …

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Apply circle theorems

O is the centre of the circle. Find x, giving reasons:Angle at centre = 100°, angle at circumference on same …

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