Angles Shape our World! What should I know? • How to measure and draw angles • How to calculate angles at a point, angles on straight line and vertically opposite angles. • How to calculate angles in triangle • How to calculate angles in quadrilateral • How to recognise parallel, intersecting and perpendicular lines • How to explain the geometrical properties of triangles and quadrilaterals. Measuring Angles Protractors have 2 scales- inner and outer 1°-180° Useful tips! 1. First you must decide if angle is acute/obtuse 2. Place the protractor exactly on the corner/point of the angle. 3. Lay the base-line of the protractor exactly along the horizontal line of the angle. Measuring Angles Measuring angles When measuring angles, make sure that the centre of the protractor is over the vertex (corner) of the angle and that the base line of the protractor is along one of the lines of the angle. www.gcsebitesize.co.uk Drawing Angles: Step 1 • Here's how to draw the angle PQR = 60° • Step1: Draw a line about 5 cm as in line QR Q R Drawing Angles: Step 2 Step 2: Place your protractor on the line QR. Ensure that the centre of your protractor is over the point Q. Make a mark at 60° Drawing Angles: Step 3 • Step 3: Remove the protractor and join Q to the 60° mark. Label this point P. Mark the angle as in diagram Reading Reflex angles •To measure reflex angles, it is easier to use a circular protractor. Drawing Angles Parts of an Angle • The corner point of an angle is called the vertex • And the two straight sides are called arms • The angle is the amount of turn between each arm. Labelling Angles 1. By giving the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta) 2. or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex). Example angle "a" is "BAC", and angle "θ" is "BCD" Important Angles! Angle Description Acute angle An angle that is less than 90° Right angle An angle that is 90° exactly Obtuse angle An angle that is greater than 90° but less than 180° Straight angle An angle that is 180° exactly Reflex angle An angle that is greater than 180° Angle Facts! • The sum of the angles around a point is 360°. • Vertically opposite angles are equal. • Vertical Angles are the angles opposite each other when two lines cross. • "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of updown. Parallel Lines • Parallel lines are lines that are equidistant, never meet and always travel in the same direction. Intersecting Lines • These are two lines that intersect at a point x X Perpendicular lines • These are two lines intersect at right angles. • The square symbol means that the angle is 90°/right angle. Simple Angle Facts • An angle measures the amount of turn and are measured in degrees. • There are 360° in a complete turn. • So in half a turn there are 180°, and in a quarter of a turn 90°. Parallel Lines and Angles • Vertically opposite angles are equal. • Corresponding angles are equal. • Alternate angles are equal. • Co-interior angles in a triangle add up to 180°. http://www.bbc.co.uk/schools/gcsebitesize/mat hs/geometry/parallellinesrev1.shtml Angles in a Triangle add to 180° Triangle Angles Sides Equilateral All angles are 60° All side equal Isosceles Two angles equal at the base Two sides are equal Right-angled One angle 90° Scalene No equal angles No equal sides Diagram Angles in a Quadrilateral-four sided figure • Sum of the angle in a quadrilateral is 360°. http://www.cimt.plymouth.ac.uk Corresponding and alternate angles
