SFR Lesson NotesThe Winston Churchill School

Circle Theorems

Geometry

38o

x

76o

x

1

2

3

70o

x

65o

x

4

Starter

Draw a circle. Draw a diameter and label it AB.

Mark any point C on the circumference. Join A, B and C to form a triangle.

Measure angle ACB. What do you find?

Repeat these steps to establish a rule.

= Circle Theorem 1: Angles in a semi­circle are 90o

Angles in a semicircle:

Draw a circle. Mark any four points on the

circumference and label them A, B, C and D. Join A, B, C and D to form a

quadrilateral. Measure the angles inside the

quadrilateral. Add the opposite angles together.

What do you find? Repeat these steps to establish a rule.

= Circle Theorem 2: Opposite angles in a cyclic quadrilateral + to 180o

Cyclic Quadrilateral

Need help?

­ mymaths: Circle Theorems

­ online textbook: pages 138 ­ 141