Properties of Shapes

Geometry at KS3 covers angles in shapes and on parallel lines, properties of polygons, congruence, similarity and the constructions needed to draw precise geometric figures.

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Angle Rules

Rule	Statement
Angles on a straight line	Sum = 180°
Angles around a point	Sum = 360°
Vertically opposite angles	Are equal
Angles in a triangle	Sum = 180°
Angles in a quadrilateral	Sum = 360°

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Angles on Parallel Lines

When a transversal crosses two parallel lines:

Angle pair	Shape formed	Relationship
Corresponding angles	F-shape	Equal
Alternate angles	Z-shape	Equal
Co-interior (same-side interior) angles	C-shape	Sum = 180°

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Triangle Types and Properties

Type	Properties
Equilateral	All sides equal; all angles 60°
Isosceles	Two sides equal; two base angles equal
Scalene	No sides or angles equal
Right-angled	One angle = 90°
Obtuse	One angle > 90°

Exterior angle of a triangle = sum of the two non-adjacent interior angles

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Quadrilaterals

Shape	Properties
Square	All sides equal; all angles 90°; 4 lines of symmetry; rotational symmetry order 4
Rectangle	Opposite sides equal; all angles 90°; 2 lines of symmetry
Parallelogram	Opposite sides parallel and equal; opposite angles equal; no lines of symmetry
Rhombus	All sides equal; opposite angles equal; diagonals bisect at right angles; 2 lines of symmetry
Trapezium	Exactly one pair of parallel sides
Kite	Two pairs of adjacent equal sides; one pair of equal angles; one line of symmetry

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Interior and Exterior Angles of Polygons

For a regular polygon with n sides:

• Sum of interior angles = (n − 2) × 180°
• Each interior angle = (n − 2) × 180° ÷ n
• Each exterior angle = 360° ÷ n
• Interior + exterior angle = 180°

Polygon	Sides	Sum of interior angles	Each interior angle (regular)
Triangle	3	180°	60°
Quadrilateral	4	360°	90°
Pentagon	5	540°	108°
Hexagon	6	720°	120°
Octagon	8	1080°	135°
Decagon	10	1440°	144°

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Congruence and Similarity