4.5.6

Angle in the Same Segment

Test yourself

Circle Theorems

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Angles in the same segment are equal

  • All triangles drawn from a chord in the same segment will have the same angle at the circumference.
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Proof

  • Draw in radii from the ends of the chord.
  • Label the angle at the centre.
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Proof continued

  • Using ‘angle at centre twice that at the circumference’ we see that
    z = 2x, z = 2y and so x = y.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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