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°.

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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

Keywords

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

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.

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).

Lesson video

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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 °.
An image in a quiz
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