New
New
Year 10
Higher

The opposite angles of a cyclic quadrilateral sum to 180°

I can derive and use the theorem: the opposite angles of a cyclic quadrilateral sum to 180°.

New
New
Year 10
Higher

The opposite angles of a cyclic quadrilateral sum to 180°

I can derive and use the theorem: the opposite angles of a cyclic quadrilateral sum to 180°.

Lesson details

Key learning points

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

Common misconception

Pupils may conflate cyclic quadrilaterals with cases of "the angle at the centre of a circle is twice the angle at the circumference" theorem, when the angle at the centre is a reflex angle.

While the two diagrams may look similar at a glance, pay extra attention to whether all four points of the quadrilateral are on the circumference or if one of the points is in the centre.

Keywords

  • Cyclic quadrilateral - A cyclic quadrilateral is a quadrilateral where all four of its vertices lie on a single circle.

The lesson demonstrates how this circle theorem could be explored practically by using a circular geoboard and using dynamic geometry software. Pupils may wish to explore these further for themselves.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Calculate the size of angle $$a$$°.
An image in a quiz
26°
Correct answer: 32°
58°
64°
128°
Q2.
The size of the angle labelled $$b$$° is °.
An image in a quiz
Correct Answer: 79, 79°, 79 degrees
Q3.
The size of the angle labelled $$c$$° is °.
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Correct Answer: 56, 56°, 56 degrees
Q4.
The size of the angle labelled $$d$$° is °.
An image in a quiz
Correct Answer: 50, 50°, 50 degrees
Q5.
∠PEF is subtended by the chord PF. ∠PFE is subtended by the chord PE. Find ∠EPD (in degrees).
An image in a quiz
Correct Answer: 92, 92°, 92 degrees
Q6.
Calculate the size of angle $$h$$°.
An image in a quiz
Correct Answer: 39, 39°, 39 degrees

6 Questions

Q1.
The size of the angle labelled $$a$$° is °.
An image in a quiz
Correct Answer: 170, 170°, 170 degrees
Q2.
Find the size of angle $$b$$°.
An image in a quiz
85°
90°
Correct answer: 95°
170°
190°
Q3.
Find the size of angle $$c$$°.
An image in a quiz
Correct answer: 83°
87°
93°
97°
Not enough information.
Q4.
The size of the angle labelled $$d$$° is °.
An image in a quiz
Correct Answer: 90, 90°, 90° degrees, right-angle
Q5.
The size of the angle labelled $$e$$° is °.
An image in a quiz
Correct Answer: 32, 32°, 32 degrees
Q6.
Find the size of angle $$g$$° (in degrees).
An image in a quiz
Correct Answer: 90, 90°, 90 degrees