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BIRKDALE HIGH SCHOOL

BIRKDALE HIGH SCHOOL. Lines and Angles. Lines and angles. Contents. A. S1.2 Parallel and perpendicular lines. A. S1.1 Labelling lines and angles. Lines. In Mathematics, a straight line is defined as having infinite length and no width. Is this possible in real life?.

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BIRKDALE HIGH SCHOOL

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  1. BIRKDALE HIGH SCHOOL Lines and Angles

  2. Lines and angles Contents • A S1.2 Parallel and perpendicular lines • A S1.1 Labelling lines and angles

  3. Lines In Mathematics, a straight line is defined as having infinite length and no width. Is this possible in real life?

  4. Labelling line segments A B When a line has end points we say that it has finite length. It is called a line segment. We usually label the end points with capital letters. For example, this line segment has end points A and B. We can call this line ‘line segment AB’.

  5. Labelling angles or ABC or B. The angle can then be described as ABC When two lines meet at a point an angle is formed. A B C An angle is a measure of the rotation of one of the line segments relative to the other. We label points using capital letters. Sometimes instead an angle is labelled with a lower case letter.

  6. Conventions, definitions and derived properties A convention is an agreed way of describing a situation. For example, we use dashes on lines to show that they are the same length. A definition is a minimum set of conditions needed to describe something. 60° For example, an equilateral triangle has three equal sides and three equal angles. 60° 60° A derived property follows from a definition. For example, the angles in an equilateral triangle are each 60°.

  7. Convention, definition or derived property?

  8. Lines in a plane What can you say about these pairs of lines? These lines do not intersect. These lines cross, or intersect. They are parallel.

  9. Lines in a plane A flat two-dimensional surface is called a plane. Any two straight lines in a plane either intersect once … This is called the point of intersection.

  10. Lines in a plane … or they are parallel. We use arrow heads to show that lines are parallel. Parallel lines will never meet. They stay an equal distance apart. We can say that parallel lines are always equidistant. Where do you see parallel lines in everyday life?

  11. Perpendicular lines What is special about the angles at the point of intersection here? a a = b = c = d b d Each angle is 90. We show this with a small square in each corner. c Lines that intersect at right angles are called perpendicularlines.

  12. Parallel or perpendicular?

  13. The distance from a point to a line What is the shortest distance from a point to a line? O The shortest distance from a point to a line is always the perpendicular distance.

  14. Angles Angles are measured in degrees. A quarter turn measures 90°. 90° It is called a right angle. We label a right angle with a small square.

  15. Angles Angles are measured in degrees. A half turn measures 180°. This is a straight line. 180°

  16. Angles Angles are measured in degrees. A three-quarter turn measures 270°. 270°

  17. Angles Angles are measured in degrees. A full turn measures 360°. 360°

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