Year 8: Geometric Reasoning Dr J Frost

Transcript:Year 8: Geometric Reasoning Dr J Frost:
Year 8: Geometric Reasoning Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 12th April 2014 Objectives: Be able to reason about sides and angles, and find interior/exterior angles of polygons. ! Sides: 3 Triangle Scalene Isosceles Equilateral 4 Quadrilateral Square Rectangle Rhombus Parallelogram Trapezium Kite 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 20 Icosagon Arrowhead ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? A polygon is a 2D shape with straight sides. ? Shape Name Lines of symmetry Num pairs of parallel sides Diagonals always equal? Diagonals perpen- dicular? Square Rectangle Kite Rhombus Parallelogram Arrowhead 4 2 1 2 0 1 2 2 0 2 2 0 Yes Yes No No No No Yes No Yes Yes No Yes ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? x = 100° y = 80° ? 50° x x = 130° 100° x y ? ? x 60° x = 120° ? 95° 55° x x = 105° ? Kite Parallelogram 1 2 3 4 Trapezium The interior angles of a quadrilateral add up to 360. ? n = 3 Total of interior angles = 180° n = 4 Total of interior angles = 360° Can you guess what the angles add up to in a pentagon? How would you prove it? We can cut a pentagon into three triangles. The sum of the interior angles of the triangles is: 3 x 180° = 540° ! For an n-sided shape, the sum of the interior angles is: 180(n-2) ? Click to Bromanimate 130° 120° 80° 160° x x = 140° ? A regular decagon (10 sides). x x = 144° ? 120° 100° 40° 40° x x = 240° ? x = 75 x = 25 x = 222 x = 309 ? ? ? ? 1a b c d e f x = 54 x = 120 x = 252 The total of the interior angles of a polygon is . How many sides does it have? The interior angle of a regular polygon is . How many sides does it have? ? ? ? g h i 2 N1 ? ? If a n-sided polygon has exactly 3 obtuse angles (i.e. 90 <  < 180), then determine