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CIRCLES PowerPoint Presentation

CIRCLES

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CIRCLES

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  1. CIRCLES BASIC TERMS AND FORMULAS Natalee Lloyd

  2. Terms Center Radius Chord Diameter Circumference Formulas Circumference formula Area formula Basic Terms and Formulas

  3. Center: The point which allpoints of the circle are equidistant to.

  4. Radius: The distance from the center to a point on the circle

  5. Chord: A segment connecting two points on the circle.

  6. Diameter: A chord that passes through the center of the circle.

  7. Circumference: The distance around a circle.

  8. Circumference Formula:C = 2r or C = dArea Formula:A = r2

  9. Circumference Example C = 2r C = 2(5cm) C = 10 cm 5 cm

  10. Area Example A = r2Since d = 14 cm then r = 7cm A = (7)2 A = 49 cm 14 cm

  11. Angles in Geometry Fernando Gonzalez - North Shore High School

  12. Intersecting Lines • Two lines that share one common point. Intersecting lines can form different types of angles.

  13. Complementary Angles • Two angles that equal 90º

  14. Supplementary Angles • Two angles that equal 180º

  15. Corresponding Angles • Angles that are vertically identical they share a common vertex and have a line running through them

  16. Geometry Basic Shapes and examples in everyday life Richard Briggs NSHS

  17. GEOMETRY Exterior Angle Sum Theorem

  18. What is the Exterior Angle Sum Theorem? • The exterior angle is equal to the sum of the interior angles on the opposite of the triangle. 40 70 70 110 110 = 70 +40

  19. Exterior Angle Sum Theorem • There are 3 exterior angles in a triangle. The exterior angle sum theorem applies to all exterior angles. 128 52 64 64 116 116 128 = 64 + 64 and 116 = 52 + 64

  20. Linking to other angle concepts • As you can see in the diagram, the sum of the angles in a triangle is still 180 and the sum of the exterior angles is 360. 160 20 100 80 80 100 80 + 80 + 20 = 180 and 100 + 100 + 160 = 360

  21. Geometry Basic Shapes and examples in everyday life Barbara Stephens NSHS

  22. GEOMETRY Interior Angle Sum Theorem

  23. What is the Interior Angle Sum Theorem? • The interior angle is equal to the sum of the interior angles of the triangle. 40 70 70 110 110 = 70 +40

  24. Interior Angle Sum Theorem • There are 3 interior angles in a triangle. The interior angle sum theorem applies to all interior angles. 128 52 64 64 116 116 128 = 64 + 64 and 116 = 52 + 64

  25. Linking to other angle concepts • As you can see in the diagram, the sum of the angles in a triangle is still 180. 160 20 100 80 80 100 80 + 80 + 20 = 180

  26. Geometry Parallel Lines with a Transversal Interior and exterior Angles Vertical Angles By Sonya Ortiz NSHS

  27. Transversal • Definition: • A transversal is a line that intersects a set of parallel lines. • Line A is the transversal A

  28. Interior and Exterior Angles • Interior angels are angles 3,4,5&6. • Interior angles are in the inside of the parallel lines • Exterior angles are angles 1,2,7&8 • Exterior angles are on the outside of the parallel lines 1 2 3 4 5 6 7 8

  29. Vertical Angles • Vertical angles are angles that are opposite of each other along the transversal line. • Angles 1&4 • Angles 2&3 • Angles 5&8 • Angles 6&7 • These are vertical angles 1 2 3 4 5 6 7 8

  30. Summary • Transversal line intersect parallel lines. • Different types of angles are formed from the transversal line such as: interior and exterior angles and vertical angles.

  31. Geometry Parallelograms M. Bunquin NSHS

  32. Parallelograms • A parallelogram is a a special quadrilateral whose opposite sides are congruent and parallel. A B D C • Quadrilateral ABCD is a parallelogram if and only if • AB and DC are both congruent and parallel • AD and BC are both congruent and parallel

  33. Kinds of Parallelograms • Rectangle • Square • Rhombus

  34. Rectangles • Properties of Rectangles • 1. All angles measure 90 degrees. • 2. Opposite sides are parallel and congruent. • 3. Diagonals are congruent and they bisect each other. • 4. A pair of consecutive angles are supplementary. • 5. Opposite angles are congruent.

  35. Squares • Properties of Square • 1. All sides are congruent. • 2. All angles are right angles. • 3. Opposite sides are parallel. • 4. Diagonals bisect each other and they are congruent. • 5. The intersection of the diagonals form 4 right angles. • 6. Diagonals form similar right triangles.

  36. Rhombus • Properties of Rhombus • 1. All sides are congruent. • 2. Opposite sides parallel and opposite angles are congruent. • 3. Diagonals bisect each other. • 4. The intersection of the diagonals form 4 right angles. • 5. A pair of consecutive angles are supplementary.

  37. Geometry Pythagorean Theorem Cleveland Broome NSHS

  38. Pythagorean Theorem • The Pythagorean theorem • This theorem reflects the sum of the squares of the sides of a right triangle that will equal the square of the hypotenuse. C2 =A2 +B2

  39. A right triangle has sides a, b and c. c b a If a =4 and b=5 then what is c?

  40. Calculations: A2 + B2 = C2 16 + 25 = 41

  41. To further solve for the length of C Take the square root of C 41 = 6.4 This finds the length of the Hypotenuse of the right triangle.

  42. The theorem will help calculate distance when traveling between two destinations.

  43. GEOMETRY Angle Sum Theorem By: Marlon Trent NSHS

  44. Triangles • Find the sum of the angles of a three sided figure.

  45. Quadrilaterals • Find the sum of the angles of a four sided figure.

  46. Pentagons • Find the sum of the angles of a five sided figure.

  47. Hexagon • Find the sum of the angles of a six sided figure.

  48. Heptagon • Find the sum of the angles of a seven sided figure.

  49. Octagon • Find the sum of the angles of an eight sided figure.

  50. Complete The Chart