The alternate segment theorem | Maths | Quizalize & Oak National Academy

Starter quiz

Find the size of angle $x$ °.

29° ✓

30.5°

61°

90°

Not enough information.
Calculate the size of angle $m$ °.

'75' ✓
Both ∠GHF and ∠GIF are angles at the circumference subtended by the chord GF. The size of the angle labelled $p$ ° is ______°.

'34' ✓
Both ∠JMK and ∠JLK are angles at the circumference subtended by the arc JK. The size of the angle labelled $t$ ° is ______°.

'76' ✓
The size of the angle labelled $a$ ° is ______°.

'28' ✓
Find the size of angle $b$ ° (in degrees).

'64' ✓

Exit quiz

Find the size of angle $a$ ° (in degrees).

35° ✓

55°

90°

110°

Not enough information.
Find the size of angle $b$ ° (in degrees).

'55' ✓
Find the size of angle $c$ ° (in degrees).

'55' ✓
The size of the angle labelled $d$ ° is ______°.

'48' ✓
∠ATC = 46° ∠ABT is subtended by the chord AT. Find the size of angle $e$ ° (in degrees).

'46' ✓
∠PEF is subtended by the chord PF. ∠PFE is subtended by the chord PE. Find ∠EPD (in degrees).

'84' ✓

Worksheet

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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

Common misconception

Pupils may conflate the alternate segment theorem with alternate angles on parallel lines, thinking that the chord that meets the tangent is a transversal between two equal angles.

Alternate angles are only equal when the transversal is between parallel lines. In many of the examples for the alternate segment theorem, the tangent is not parallel to a chord.

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.
Segment - Two segments are created when dividing a circle into two parts using a chord.
Tangent - A tangent of a circle is a line that intersects the circle exactly once.