Myths about teaching can hold you back
- Year 10•
- Higher
The alternate segment theorem
I can derive and use the theorem: the alternate segment theorem.
- Year 10•
- Higher
The alternate segment theorem
I can derive and use the theorem: the alternate segment theorem.
Lesson details
Key learning points
- 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
Keywords
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 misconception
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.
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.
To help you plan your year 10 maths lesson on: The alternate segment theorem, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The alternate segment theorem, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Circle theorems unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Find the size of angle $$x$$°.
Q2.Calculate the size of angle $$m$$°.
Q3.Both ∠GHF and ∠GIF are angles at the circumference subtended by the chord GF.
The size of the angle labelled $$p$$° is °.
Q4.Both ∠JMK and ∠JLK are angles at the circumference subtended by the arc JK.
The size of the angle labelled $$t$$° is °.
Q5.The size of the angle labelled $$a$$° is °.
Q6.Find the size of angle $$b$$° (in degrees).
Assessment exit quiz
6 Questions
Q1.Find the size of angle $$a$$° (in degrees).
Q2.Find the size of angle $$b$$° (in degrees).
Q3.Find the size of angle $$c$$° (in degrees).
Q4.The size of the angle labelled $$d$$° is °.
Q5.∠ATC = 46°
∠ABT is subtended by the chord AT.
Find the size of angle $$e$$° (in degrees).
Q6.∠PEF is subtended by the chord PF.
∠PFE is subtended by the chord PE.
Find ∠EPD (in degrees).
