Geometry 2 polygons
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This document defines and provides key information about different types of polygons. It discusses polygons in general, then focuses on quadrilaterals. It defines triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, and decagons. It then discusses properties of special quadrilaterals including parallelograms, rectangles, squares, rhombi, kites, and trapezoids. It provides the sufficient conditions to prove each type of polygon or quadrilateral and includes examples.
Geometry 2 polygons
- 2. Polygons Quadrilaterals Sufficient conditions Polygons Polygons Sum of the interior angles of a polygon with n sides = (n – 2)180º Sum of the exterioranglesof any polygon = 360º A regular polygon is a polygon with equal sidesand therefore equal anglestoo. Every interior angle of a regular polygon with nsides 360o n . Polygons . Important formulas concerning polygons: n Every exterior angle of a regular polygon with nsides = 2 o = (n 2)180
- 3. Names ofpolygons Triangle (3sides) Quadrilateral(4sides) Pentagon(5sides) Hexagon(6sides) Heptagon(7sides) Octagon (8sides) Nonagon(9sides) Decagon (10sides) Example Find the size of the angles indicated by letters: FlashCard Quadrilateral 4 sides, 4 angles FlashCard Quadrilateral (4) A Quad Bike has 4 wheels FlashCard 3
- 4. FlashCard pentagon 5 sides, 5 angles FlashCard FlashCard pentagon 5 sides, 5 angles Buckyball: 12 pentagons (see black patches), 20 hexagons FlashCard Hexagon 6 sides, 6 angles FlashCard heXagon 6 sides, 6angles FlashCard 4 Think X: siX
- 5. FlashCard hexagon 6 sides, 6angles Buckyball: 12 pentagons, 20 hexagons (see white patches) FlashCard heptagon 7 sides, 7 angles FlashCard heptagon 7 sides, 7angles FlashCard FlashCard octagon 8 sides, 8 angles FlashCard 5
- 6. octagon think octopus FlashCard octagon 8 sides, 8angles FlashCard 4 Special Quadrilaterals •TheParallelogram A four-sided polygon with two pairs ofparallel and equal sides. •Rectangle: A rectangle is a parallelogram with rightangles. • Square: A square is a rectangle with 4 equalsides. •Rhombus: A rhombus is a parallelogram with 4 equal sides. Special Quadrilaterals • Trapezium: A trapezium is a quadrilateral with only one pairof parallel sides • Kite: A quadrilateral in which two pairs of adjacent sides are equal The familytree 6
- 7. SpecialQuadrilaterals:properties Example Find the values of x andy. Given: AD║BC Find the values of x andy. Exercise Findx Parallelogram Sufficient conditions to provea parallelogram Prove one of the following: • Both pairs of opposite sides parallel • Both pairs of opposite sides equal • Both pairs of opposite angles equal • Diagonals bisect each other • One pair of opposite sides parallel and equal 7
- 8. Rectangle Sufficient conditions to provea rectangle • Prove the quadrilateral is a parallelogram AND one interior angle equals 𝟗𝟎° Rhombus Sufficient conditions to provea rhombus • Prove the quadrilateral is a parallelogram AND one pair of adjacent sides are equal Square Sufficient conditions to provea square • Prove the quadrilateral is a parallelogram AND one interior angle equals 𝟗𝟎° AND one pair of adjacent sides is equal 8
- 9. Kite Sufficient conditions to provea kite •Prove that two pairs of adjacent sides are equal • Remember: NOT a parallelogram Trapezium Sufficient conditions to provea trapezium •Prove that one pair of opposite sides are parallel • Remember: NOT a parallelogram Example: ABCD is a parallelogram with DF = EB. Prove that AECF is a parallelogram. Complete the following statements: 9 2. 3. 4. 5. 1 If the diagonals of a quadrilateral are not equal, but bisect each other perpendicularly, the quadrilateral is a……… A triangle that has three equal sides is called an ….… triangle. If both pairs of adjacent sides of a quadrilateral are equal, but the opposite sides are not equal, the quadrilateral is a ……. If the diagonals of a quadrilateral are equal and bisect each other perpendicularly, the quadrilateral is a….… If both pairs of opposite angles of a quadrilateral are equal, the quadrilateral is a ……