UNIT 3 Angle Geometr Overhead Slides Overhead Slides 3.1 Triangles 3.2 Special Quadrilaterals 3.3 Angles and Parallel Lines 3.4 Geometrical Properties of Circles 3.5 Tangent-Circle Properties 3.6 3-D Shapes 3.7 Compass Direction and Bearings
OS 3.1 Triangles A triangle is a polgon with 3 sides. Triangles can be classified according to: (a) length of sides Scalene Triangle Isosceles Triangle Equilateral Triangle No sides are of Two sides are of All sides are of equal length. equal length. equal length. (b) size of angles Acute-angled Right-angled Obtuse-angled Triangle Triangle Triangle All angles are One angle is a One angle is an acute angles right angle obtuse angle (less than 90 ) (90 ) (greater than 90 )
OS 3.2 Special Quadrilaterals Quadrilateral Parallelogram Rectangle Rhombus Kite Trapezium Square Quadrilateral Sides Angles Diagonals Parallelogram Both pairs of Both pairs of Diagonals bisect opposite sides are opposite angles each other. equal and parallel are equal. Rectangle Both pairs of All 4 angles Diagonals bisect opposite sides are are right angles. each other and equal and parallel. are equal. Square All 4 sides equal. All 4 angles Diagonals bisect Opposite sides are right angles. each other at right are parallel. angles and are equal. Rhombus All 4 sides equal. Both pairs of Diagonals bisect Opposite sides opposite angles each other at are parallel. are equal. right angles. Kite Two pairs of Onl one pair of Longer diagonal adjacent sides are opposite angles bisects shorter equal but not all are equal. diagonal at right 4 sides are equal. angles. Trapezium One pair of opposite sides are parallel.
OS 3.2 Special Quadrilaterals Quadrilateral Sides Angles Diagonals Parallelogram Both pairs of Both pairs of Diagonals bisect opposite sides are opposite angles each other. equal and parallel are equal. Rectangle Both pairs of All 4 angles Diagonals bisect opposite sides are are right angles. each other and equal and parallel. are equal. Square All 4 sides equal. All 4 angles Diagonals bisect Opposite sides are right angles. each other at right are parallel. angles and are equal. Rhombus All 4 sides equal. Both pairs of Diagonals bisect Opposite sides opposite angles each other at are parallel. are equal. right angles. Kite Two pairs of Onl one pair of Longer diagonal adjacent sides are opposite angles bisects shorter equal but not all are equal. diagonal at right 4 sides are equal. angles. Trapezium One pair of opposite sides are parallel.
OS 3.3 Angles and Parallel Lines a d b c g f h e Results Corresponding angles are equal. e.g. d = f, c = e Alternate angles are equal. e.g. b = f, a = e Supplementar angles sum to 180. e.g. a + f = 180 Thus If corresponding angles are equal, then the two lines are parallel. If alternate angles are equal, then the two lines are parallel. If supplementar angles sum to 180, then the two lines are parallel.
OS 3.4 Geometrical Properties of Circles A straight line drawn from the centre of a circle to bisect a chord is perpendicular to the chord. a b Equal length chords are equidistant from the centre of the circle. = if a = b An angle at the centre of a circle is twice an angle at the circumference subtended b the arc. = 2 Ever angle subtended b the diameter of a semi-circle is a right angle. Angles subtended b a chord in the same segment of a circle are equal. =
OS 3.5 Tangent-Circle Properties A tangent to a circle is perpendicular to the radius drawn to the point of contact. a a b = b = Tangents drawn to a circle from an eternal point are equal. The line joining the point to the centre of the circle bisects the angle between the tangents. The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. =
OS 3.6 3-D Shapes
OS 3.7 Compass Direction and Bearings N NW 315 NE W 270 045 090 E 225 180 135 SW SE S