1 / 25

PART 3 Angle Relationships

PART 3 Angle Relationships. Angle Relationships. Lesson Objectives - Students will: Discover angle properties such as: Complementary, Supplementary, vertically opposite, Corresponding, Alternate, interior. Investigate properties of triangles and quadrilaterals.

jerome
Download Presentation

PART 3 Angle Relationships

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PART 3 Angle Relationships

  2. Angle Relationships • Lesson Objectives - Students will: • Discover angle properties such as: Complementary, Supplementary, vertically opposite, Corresponding, Alternate, interior. • Investigate properties of triangles and quadrilaterals

  3. 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.

  4. 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.

  5. Complementary and supplementary angles Two supplementary angles add up to 180°. Two complementary angles add up to 90°. a b a b a + b = 90° a + b = 180°

  6. Angles on a straight line

  7. Angles around a point

  8. 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.

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

  10. 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

  11. Angles and parallel lines

  12. Angles made with parallel lines

  13. Calculating angles Calculate the size of angle a. 28º Hint: Add another parallel line. a 45º 73º a = 28º + 45º =

  14. Interior and exterior angles in a triangle

  15. Calculating angles Calculate the size of the lettered angles in each of the following triangles. 116° b 33° a 82° 64° 34° 31° 43° c 25° d 131° 152° 127° 272°

  16. Interior angles in polygons b c a The angles inside a polygon are called interior angles. The sum of the interior angles of a triangle is 180°.

  17. Angles in a triangle We can prove that the sum of the angles in a triangle is 180° by drawing a line parallel to one of the sides through the opposite vertex. a b c a b These angles are equal because they are alternate angles. Call this angle c. a + b + c = 180° because they lie on a straight line. The angles a, b and c in the triangle also add up to 180°.

  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. Calculating angles Calculate the size of the lettered angles in each of the following triangles. 116° b 33° a 82° 64° 34° 31° 43° c 25° d 131° 152° 127° 272°

  20. Calculating angles Calculate the size of the lettered angles in this diagram. 38º 38º 56° 73° 86° a b 69° 104° Base angles in the isosceles triangle = (180º – 104º) ÷ 2 = 76º ÷ 2 = 38º = 86º Angle a = 180º – 56º – 38º = 69º Angle b = 180º – 73º – 38º

  21. Sum of the interior angles in a quadrilateral What is the sum of the interior angles in a quadrilateral? d c f a e b We can work this out by dividing the quadrilateral into two triangles. a + b + c = 180° and d + e + f = 180° So, (a + b + c)+ (d + e + f )= 360° The sum of the interior angles in a quadrilateral is 360°.

  22. Sum of interior angles in a polygon We have just shown that the sum of the interior angles in any quadrilateral is 360°. d a c b We already know that the sum of the interior angles in any triangle is 180°. c a + b + c = 180 ° a b a + b + c + d = 360 ° Do you know the sum of the interior angles for any other polygons?

  23. Sum of the interior angles in a polygon We’ve seen that a quadrilateral can be divided into two triangles … … a pentagon can be divided into three triangles … … and a hexagon can be divided into four triangles. How many triangles can a hexagon be divided into?

  24. Interior angles in regular polygons A regular polygon has equal sides and equal angles. We can work out the size of the interior angles in a regular polygon as follows: Equilateral triangle 180° 180° ÷ 3 = 60° Square 2 × 180° = 360° 360° ÷ 4 = 90° Regular pentagon 3 × 180° = 540° 540° ÷ 5 = 108° Regular hexagon 4 × 180° = 720° 720° ÷ 6 = 120°

  25. Sum of the interior angles in a polygon The number of triangles that a polygon can be divided into is always two less than the number of sides. We can say that: A polygon with n sides can be divided into (n– 2) triangles. The sum of the interior angles in a triangle is 180°. So, The sum of the interior angles in an n-sided polygon is (n– 2) × 180°.

More Related