Symmetry And Shapes

## Symmetry & Shapes - Quick Revision ### Lines & Angles - **Acute angle**: < 90° - **Right angle**: exactly 90° - **Obtuse angle**: > 90° and < 180° - **Straight angle**: exactly 180° - **Reflex angle**: > 180° and < 360° - Angles at a point sum to 360°; angles on a straight line sum to 180°. - **Parallel lines** never meet (marked with arrows). - **Perpendicular lines** intersect at 90°. ### Rotational Symmetry - **Order of rotational symmetry**: number of times a shape looks the same in a full 360° turn. - Use tracing paper with an arrow to check. - Order 1 means no rotational symmetry. - Regular polygons: order = number of sides. ### Lines of Symmetry - A line that divides a shape into two mirror halves. - Regular polygons: number of lines = number of sides. - Square: 4 lines; rectangle: 2 lines; rhombus: 2 lines; kite: 1 line; trapezium: 0 (isosceles trapezium: 1). ### Polygons (2D Shapes) - **Triangle**: 3 sides (equilateral, isosceles, right-angled, scalene). - **Quadrilateral**: 4 sides (square, rectangle, parallelogram, rhombus, trapezium, kite). - **Pentagon**: 5 sides; **Hexagon**: 6; **Heptagon**: 7; **Octagon**: 8; **Nonagon**: 9; **Decagon**: 10. - **Regular polygon**: all sides equal, all angles equal. ### Quadrilateral Properties - **Square**: 4 equal sides, 4 right angles, 4 lines of symmetry, rotational order 4. - **Rectangle**: opposite sides equal, 4 right angles, 2 lines of symmetry, rotational order 2. - **Parallelogram**: opposite sides parallel and equal, opposite angles equal, 0 lines of symmetry, rotational order 2. - **Rhombus**: all sides equal, opposite angles equal, 2 lines of symmetry, rotational order 2. - **Trapezium**: one pair of parallel sides, 0 lines of symmetry (isosceles: 1 line), rotational order 1. - **Kite**: two pairs of equal adjacent sides, one pair of equal opposite angles, 1 line of symmetry, rotational order 1. ### Circles - **Circumference**: perimeter of circle. - **Diameter**: line through centre, 2 × radius. - **Radius**: centre to circumference. - **Chord**: line joining two points on circumference. - **Arc**: part of circumference. - **Sector**: region between two radii and an arc. - **Segment**: region between a chord and an arc. - **Tangent**: line touching circle at one point. - Diameter = 2 × Radius. ### 3D Shapes - **Cube**: 6 square faces, 12 edges, 8 vertices. - **Cuboid**: 6 rectangular faces, 12 edges, 8 vertices. - **Triangular prism**: 2 triangular faces, 3 rectangular faces, 9 edges, 6 vertices. - **Square-based pyramid**: 1 square face, 4 triangular faces, 8 edges, 5 vertices. - **Tetrahedron**: 4 triangular faces, 6 edges, 4 vertices. - **Cylinder**: 2 circular faces, 1 curved face. - **Cone**: 1 circular face, 1 curved face. - **Sphere**: 1 curved face. ### Nets of Solids - A net is a 2D pattern that folds to form a 3D shape. - **Cube net**: 6 squares (common cross shape). - **Cuboid net**: 6 rectangles in three pairs. - **Cylinder net**: two circles + a rectangle (length = circumference). - **Square-based pyramid net**: 1 square + 4 triangles. - Surface area of solid = area of its net.