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KS3 Mathematics

KS3 Mathematics. S1 Lines and Angles. S1 Lines and angles. Contents. S1.1 Labelling lines and angles. S1.2 Parallel and perpendicular lines. S1.3 Calculating angles. S1.4 Angles in polygons. Lines in a plane. What can you say about these pairs of lines?. These lines do not intersect.

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KS3 Mathematics

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  1. KS3 Mathematics S1 Lines and Angles

  2. S1 Lines and angles Contents S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons

  3. 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.

  4. 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.

  5. 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. This means that they are always equidistant. Where do you see parallel lines in everyday life?

  6. 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.

  7. Types of angle Rightangle a= 90º Acute angle 0º < a < 90º a a Obtuseangle 90º < a < 180º Reflex angle180º < a < 360º a a

  8. Angles on a straight line and at a point a Angles at a point add up to 360 Angles on a line add up to 180 b b d c a c a + b + c = 180° a + b + c + d = 360 because there are 180° in a half turn. because there are 360 in a full turn.

  9. Vertically opposite angles a d b c When two lines intersect, two pairs of vertically opposite angles are formed. and a = c b = d Vertically opposite angles are equal.

  10. Intersecting lines

  11. Angles on a straight line

  12. Angles on a straight line Angles on a line add up to 180. a b a + b = 180° because there are 180° in a half turn.

  13. Angles around a point

  14. Angles around a point Angles around a point add up to 360. b a c d a + b + c + d = 360 because there are 360 in a full turn.

  15. Calculating angles around a point Use geometrical reasoning to find the size of the labelled angles. 69° 68° d 167° a 43° c 43° b 103° 137°

  16. Angles in a triangle c a b For any triangle, a + b + c = 180° The angles in a triangle add up to 180°.

  17. Angles in a triangle

  18. Calculating angles in a triangle Calculate the size of the missing angles in each of the following triangles. 64° b 116° 33° a 326° 31° 82° 49° 43° 25° d 88° c 28° 233°

  19. Angles in an isosceles triangle In an isosceles triangle, two of the sides are equal. We indicate the equal sides by drawing dashes on them. The two angles at the bottom on the equal sides are called base angles. The two base angles are also equal. If we are told one angle in an isosceles triangle we can work out the other two.

  20. Angles in an isosceles triangle 46° 46° For example, 88° a a Find the size of the other two angles. The two unknown angles are equal so call them both a. We can use the fact that the angles in a triangle add up to 180° to write an equation. 88° + a + a = 180° 88° + 2a = 180° 2a = 92° a = 46°

  21. Interior and exterior angles in a triangle

  22. Corresponding, alternate and interior angles Corresponding angles are equal Alternate angles are equal Interior angles add up to 180° a a a b b b a = b a = b a + b = 180° Look for an F-shape Look for a Z-shape Look for a C- or U-shape

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