Myths about teaching can hold you back
- Year 10•
- Higher
The angles in the same segment are equal
I can derive and use the theorem: the angles in the same segment are equal.
- Year 10•
- Higher
The angles in the same segment are equal
I can derive and use the theorem: the angles in the same segment are equal.
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.
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 misconception
Pupils may reason that two angles are the same size, as they are subtended by the same chord.
Angles are equal, if they are in the same segment, subtended by the same arc, as well as subtended by the same chord.
To help you plan your year 10 maths lesson on: The angles in the same segment are equal, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The angles in the same segment are equal, 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
Prior knowledge starter quiz
6 Questions
Q1.An angle at the circumference of a circle is subtended by the diameter of that circle.
What is the size of this angle (in degrees)?
Q2.The size of the angle labelled $$x$$° is °.

Q3.The size of the angle labelled $$y$$° is °.

Q4.The size of the angle labelled $$z$$° is °.

Q5.The image shows a circle with centre O. A triangle is formed from two radii and a chord. A tangent to the circle is shown. 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 $$x$$° on this 18-point geoboard.

Q2.Find the size of angle $$y$$° on this 18-point geoboard (in degrees).

Q3.The image shows an 18 point geoboard. The size of the angle labelled $$z$$° is °.

Q4.Both ∠ACB and ∠ADB are angles at the circumference subtended by the chord AB.
The size of the angle labelled $$k$$° is °.

Q5.Both ∠GHF and ∠GIF are angles at the circumference subtended by the chord GF.
The size of the angle labelled $$p$$° is °.

Q6.Both ∠JMK and ∠JLK are angles at the circumference subtended by the arc JK.
The size of the angle labelled $$t$$° is °.
