Myths about teaching can hold you back
- Year 10•
- Higher
The angle in a semicircle is a right angle
I can derive and use the theorem: the angle in a semicircle is a right angle.
- Year 10•
- Higher
The angle in a semicircle is a right angle
I can derive and use the theorem: the angle in a semicircle is a right angle.
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
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.
Arc - An arc of a circle is part of the circle’s circumference.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Diameter - The diameter of a circle is any line segment that starts and ends on the circumference of the circle and passes through the centre of the circle.
Common misconception
Pupils may over-generalise the circle theorem by assume that all triangles that are inscribed in a circle are right-angled.
The triangle is only right-angled if one of its angles is subtended by the diameter. This also means that if the triangle is right-angled, then its hypotenuse is the diameter of the circle.
To help you plan your year 10 maths lesson on: The angle in a semicircle is a right angle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The angle in a semicircle is a right angle, 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.A chord has endpoints of A and B.
Where on the circle must points A and B lie?
Q2.The size of the angle labelled $$x$$° on this 20-point geoboard is °.

Q3.The size of the angle labelled $$y$$° on this 20-point geoboard is °.

Q4.The size of the angle labelled $$z$$° on this 20-point geoboard is °.

Q5.What is the size of the angle subtended by the chord AC (in degrees)?

Q6.The size of the angle labelled $$m$$° is °.

Assessment exit quiz
6 Questions
Q1.Find the size of angle $$a$$° on this 8-point geoboard (in degrees).

Q2.Find the size of angle $$b$$° on this 8-point geoboard (in degrees).

Q3.The size of the angle labelled $$c$$° on this 8-point geoboard is °.

Q4.The size of the angle $$(b+d)$$° on this 8-point geoboard is °.

Q5.The size of the angle labelled $$x$$° is °.

Q6.Chord AB has length of 4 cm.
The length of chord BC is cm (2 d.p.).
