Circle Theorems + angle rules
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24 Terms
Two ____ from the centre make triangle OAB ____, so the base angles are equal
Two radii from the centre make triangle OAB isosceles, so the base angles are equal:
Angle at the centre = ____ × angle at the circumference, on the same ____.
Angle at the centre = 2 × angle at the circumference, on the same arc.
Angle in a semicircle = ____°, because AB is a ____.
Angle in a semicircle = 90°, because AB is a diameter.
Angles in the ____ segment (same chord, same side) are ____.
Angles in the same segment (same chord, same side) are equal.
Opposite angles in a cyclic quadrilateral add up to ____°.
Opposite angles in a cyclic quadrilateral add up to 180°.
A radius meets a tangent at ____°.
A radius meets a tangent at 90°.
Tangents from an external point are ____ in length.
Tangents from an external point are equal in length.
A perpendicular from the centre ____ the chord.
A perpendicular from the centre bisects the chord.
Tangent-chord angle = angle in the ____ segment.
Tangent-chord angle = angle in the alternate segment.
Angles on a straight line add up to ____°.
Angles on a straight line add up to 180
Angles around a point add up to ____°.
Angles around a point add up to 360°.
Vertically opposite angles are ____.
Vertically opposite angles are equal.
Angles in a triangle add up to ____°.
Angles in a triangle add up to 180°.
In an isosceles triangle the ____ angles are equal.
In an isosceles triangle the base angles are equal.
In an equilateral triangle every angle is ____°.
In an equilateral triangle every angle is 60°.
Angles in a quadrilateral add up to ____°.
Angles in a quadrilateral add up to 360°.
Parallel lines: ____ angles are equal (F shape).
Parallel lines: corresponding angles are equal (F shape).
Parallel lines: ____ angles are equal (Z shape).
Parallel lines: alternate angles are equal (Z shape).
Parallel lines: ____ (allied) angles add up to ____° (C shape).
Parallel lines: co-interior (allied) angles add up to 180° (C shape).
Sum of interior angles of a polygon = (____ − 2) × ____°.
Sum of interior angles of a polygon = (n − 2) × 180°.
Exterior angles of any polygon add up to ____°.
Exterior angles of any polygon add up to 360°.
Regular polygon: each exterior angle = ____ ÷ n.
Regular polygon: each exterior angle = 360 ÷ n.
Interior angle + exterior angle at a vertex = ____°.
Interior angle + exterior angle at a vertex = 180°.
Regular polygon: each interior angle = ____ − exterior angle, or (n − 2) × 180 ÷ n.
Regular polygon: each interior angle = 180 − exterior angle, or
(n − 2) × 180 ÷ n.