Properties of ShapesAQA GCSE Maths: Flashcards

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What is the sum of angles at a point?

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What is the sum of angles at a point?: The sum of angles at a point is 360°.
What is the sum of angles on a straight line?: The sum of angles on a straight line is 180°.
Define vertically opposite angles and state their property.: Vertically opposite angles are angles formed opposite each other when two straight lines intersect. Vertically opposite angles are equal.
Name the three angle properties in parallel lines cut by a transversal.: Alternate angles are equal; corresponding angles are equal; co-interior angles (same-side interior angles) sum to 180°.
What is the sum of interior angles in a triangle?: The sum of interior angles in a triangle is 180°.
Derive the sum of interior angles in a polygon with n sides.: The sum of interior angles in an n-sided polygon is (n − 2) × 180°.
What are the properties of an isosceles triangle?: An isosceles triangle has two equal sides and two equal base angles opposite those sides.
Define the properties of a cyclic quadrilateral.: A cyclic quadrilateral is a quadrilateral inscribed in a circle. Opposite angles in a cyclic quadrilateral sum to 180°.
What is a regular polygon and what property do its interior angles share?: A regular polygon has all sides equal and all angles equal. Each interior angle of a regular n-sided polygon is (n − 2) × 180° ÷ n.
State the relationship between exterior angles of any polygon.: The sum of exterior angles of any polygon is 360°. Each exterior angle of a regular n-sided polygon is 360° ÷ n.
Define a tangent to a circle and state its key property.: A tangent is a straight line that touches the circle at exactly one point. A tangent to a circle is perpendicular to the radius at the point of contact.
State the Angle at Centre Theorem for circles.: The angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any point on the circumference.
What does the Angles in the Same Segment Theorem state?: Angles subtended by the same arc at the circumference of a circle are equal.
State the Alternate Segment Theorem.: The angle between a tangent and a chord at the point of contact is equal to the angle subtended by the chord in the alternate segment.
Define the key circle terms: radius, diameter, chord, arc, sector, and segment.: Radius: distance from centre to circumference; Diameter: distance across circle through centre (2r); Chord: straight line joining two points on circumference; Arc: part of circumference; Sector: region bounded by two radii and an arc; Segment: region bounded by a chord and an arc.