Study Guides

Unit Summary

In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

Lesson Summary

You will learn to derive and use the theorem: the angles in the same segment are equal.

Key Notes

• A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
• Theorems can be thought of as puzzles to solve, you are showing how to find a result
• In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Vocabulary To Learn

• Theorem: A theorem is a statement that can be proved using known mathematical facts and reasoning.
• Subtended: An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.
• Chord: A chord is any line segment joining two points on the circumference of a circle.
• Segment: Two segments are created when dividing a circle into two parts using a chord.

Common Mistakes To Avoid

• Pupils may reason that two angles are the same size, as they are subtended by the same chord.

3 Quick Questions (With Answers)

More Lessons In This Unit

• Checking and securing understanding of the parts of a circle Study Guide
• Identifying which circle theorem to use Study Guide
• Problem solving with circle theorems Study Guide
• The alternate segment theorem Study Guide
• The angle at the centre of the circle is twice the angle at any point on the circumference Study Guide
• The angle in a semicircle is a right angle Study Guide
• The opposite angles of a cyclic quadrilateral sum to 180° Study Guide
• The perpendicular from the centre of a circle to a chord bisects the chord Study Guide
• The tangent at any point on a circle is perpendicular to the radius at that point Study Guide
• The tangents from an external point are equal in length Study Guide