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Algebra A

Algebra A. Lines and Angles. Lines. In Mathematics, a straight line is defined as having infinite length and no width. Is this possible in real life?. Labelling line segments. A. B. When a line has end points we say that it has finite length. It is called a line segment.

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Algebra A

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  1. Algebra A Lines and Angles

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

  3. 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’.

  4. Labelling angles or CBA. 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.

  5. 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.

  6. 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.

  7. 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?

  8. 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.

  9. 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.

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

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

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

  13. Learn facts about Angles between intersecting lines Angles on a straight line Angles around a point You must learn facts about angles.So you can calculate their size without drawing or measuring.

  14. 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.

  15. 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.

  16. 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.

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

  18. Complementary angles When two angles add up to 90° they are called complementary angles. a b a + b = 90° Angle a and angle b are complementary angles.

  19. Supplementary angles When two angles add up to 180° they are called supplementary angles. b a a + b = 180° Angle a and angle b are supplementary angles.

  20. Angles made with parallel lines When a straight line crosses two parallel lines eight angles are formed. a b d c e f h g Which angles are equal to each other?

  21. Corresponding angles There are four pairs of corresponding angles, or F-angles. a a b b d d c c e e f f h h g g d = h because Corresponding angles are equal

  22. Corresponding angles There are four pairs of corresponding angles, or F-angles. a a b b d d c c e e f f h h g g a = e because Corresponding angles are equal

  23. Corresponding angles There are four pairs of corresponding angles, or F-angles. a b d c c e f h g g c = g because Corresponding angles are equal

  24. Corresponding angles There are four pairs of corresponding angles, or F-angles. a b b d c e f f h g b = f because Corresponding angles are equal

  25. Alternate angles There are two pairs of alternate angles, or Z-angles. a b d d c e f f h g d = f because Alternate anglesare equal

  26. Alternate angles There are two pairs of alternate angles, or Z-angles. a b d c c e e f h g c = e because Alternate anglesare equal

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

  28. 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°

  29. 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 of 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.

  30. Angles in an isosceles triangle 46° 46° For example, 88° a a Find the sizes 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°

  31. Interior angles in triangles b c a The angles inside a triangle are called interior angles. The sum of the interior angles of a triangle is 180°.

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