Proof - Circle Theorems Flashcards
Theorem 2 - angles at edge and centre
The angle subtended at the centre of a circle is twice the angle subtended at the circumference (in the same arc)
The angles do not have to be opposite each other, just as long as they are created by the same two lines
Theorem 3 - equal angles (segments)
Angles at the circumference via the same arc are equal
(Angles in the same segment are equal)
Makes a ‘bow tie’ shape
Theorem 4 -quadrilateral
Opposite angles in a cyclic quadrilateral (quadrilateral made in a circle) add up to 180°
Theorem 5 - radius
Where a tangent meets a radius a there is a right angle
Theorem 6 - tangent length
Two tangents meet at equal length
Two tangents (originating from opposite positions) meet at an equal length
Theorem 6 - alternate segments
Angles in alternate segments are equal
What are alternate angles
Angles formed when a line passes through two parallel lines
seen in a ‘z’ pattern
The angles on the inside of the ‘z’ bend are equal
What are corresponding angles
Angles in matching corners.
Formed when a line intersects two parallel lines
Also known as the ‘F’ rule
The angles directly attached under the horizontal lines are equal
(The ones above are also equal)
Theorem 1 -semicircle
Angles subtended to the circumference from edges of a semi - circle are 90
