Year 10 - Maths
The alternate segment theorem
Circle theorems
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
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 alternate segment theorem.
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.
- Segment: Two segments are created when dividing a circle into two parts using a chord.
- Tangent: A tangent of a circle is a line that intersects the circle exactly once.
Common Mistakes To Avoid
- Pupils may conflate the alternate segment theorem with alternate angles on parallel lines, thinking that the chord that meets the tangent is a transversal between two equal angles.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
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.
2. Use this key word in a maths sentence and explain it clearly. 'Theorem'
A theorem is a statement that can be proved using known mathematical facts and reasoning. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may conflate the alternate segment theorem with alternate angles on parallel lines, thinking that the chord that meets the tangent is a transversal between two equal angles. Correction: Alternate angles are only equal when the transversal is between parallel lines. In many of the examples for the alternate segment theorem, the tangent is not parallel to a chord.
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 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 angles in the same segment are equal 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
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