New
New
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.

New
New
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.

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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

  • 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.

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.
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)?
30°
45°
60°
Correct answer: 90°
Not enough information.
Q2.
The size of the angle labelled $$x$$° is °.
An image in a quiz
Correct Answer: 162, 162°, 162 degrees
Q3.
The size of the angle labelled $$y$$° is °.
An image in a quiz
Correct Answer: 81, 81°, 81 degrees
Q4.
The size of the angle labelled $$z$$° is °.
An image in a quiz
Correct Answer: 81, 81°, 81 degrees
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 °.
An image in a quiz
Correct Answer: 31, 31°, 31 degrees
Q6.
Find the size of angle $$b$$° (in degrees).
An image in a quiz
Correct Answer: 59, 59°, 59 degrees

6 Questions

Q1.
Find the size of angle $$x$$° on this 18-point geoboard.
An image in a quiz
18°
20°
Correct answer: 80°
90°
Q2.
Find the size of angle $$y$$° on this 18-point geoboard (in degrees).
An image in a quiz
Correct Answer: 40, 40°, 40 degrees
Q3.
The image shows an 18 point geoboard. The size of the angle labelled $$z$$° is °.
An image in a quiz
Correct Answer: 40, 40°, 40 degrees
Q4.
Both ∠ACB and ∠ADB are angles at the circumference subtended by the chord AB. The size of the angle labelled $$k$$° is °.
An image in a quiz
Correct Answer: 31, 31°, 31 degrees
Q5.
Both ∠GHF and ∠GIF are angles at the circumference subtended by the chord GF. The size of the angle labelled $$p$$° is °.
An image in a quiz
Correct Answer: 38, 38°, 38 degrees
Q6.
Both ∠JMK and ∠JLK are angles at the circumference subtended by the arc JK. The size of the angle labelled $$t$$° is °.
An image in a quiz
Correct Answer: 71, 71°, 71 degrees