1. BASIC TERMS AND FORMULAS Natalee Lloyd
CIRCLES
BASIC TERMS AND FORMULAS
Natalee Lloyd

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

3. Center: The point which all points 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 = d Area Formula: A = r2

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

10. Area Example A = r2 Since d = 14 cm then r = 7cm A = (7)2 A = 49 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. Basic Shapes and examples in everyday life
Geometry
Basic Shapes
and examples in everyday life
Richard Briggs
NSHS

17. Exterior Angle Sum Theorem
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 =

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 = and 116 =

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
= 180 and = 360

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

22. Interior Angle Sum Theorem
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 =

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 = and 116 =

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
= 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.
If a =4 and b=5 then what is c?

40. Calculations:
A2 + B2 = C2
= 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. Angle Sum Theorem By: Marlon Trent NSHS
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 Triangle Quadrilateral Pentagon Hexagon Heptagon
Name of figure
Number of sides
Sum of angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Decagon
n-agon

51. What is the angle sum formula?
Angle Sum=(n-2)180 Or
Angle Sum=180n-360

52. A presentation by
Mary McHaney

53. THE SQUARE IS A RECTANGLE OR THE RECTANGLE IS A SQUARE
A SQUARE IS RECTANGLE
QUADRILATERAL DILEMMA
THE SQUARE IS A RECTANGLE OR
THE RECTANGLE IS A SQUARE

54. SQUARE Characteristics:
Four equal sides
Four Right Angles

55. RECTANGLE Characteristics
Opposite sides are equal
Four Right Angles

56. Square and Rectangle share
Four right angles
Opposite sides are equal

57. SQUARE AND RECTANGLE DO NOT SHARE:
All sides are equal

58. SO
A SQUARE IS RECTANGLE
A RECTANGLE IS NOT A SQUARE

59. Charles Upchurch

60. Triangles Are Classified Into 2 Main Categories.
Types of Triangles
Triangles Are Classified Into 2 Main Categories.

61. Triangles Classified by Sides

62. Triangles Classified by Their Sides Scalene Triangles
These triangles have all 3 sides of different lengths.

63. Isosceles Triangles
These triangles have at least 2 sides of the same length. The third side is not necessarily the same length as the other 2 sides.

64. Equilateral Triangles
These triangles have all 3 sides of the same length.

65. Triangles Classified by their Angles

66. Acute Triangles
These Triangles Have All Three Angles That Each Measure Less Than 90 Degrees.

67. Right Triangles
These triangles have exactly one angle that measures 90 degrees. The other 2 angles will each be acute.

68. Obtuse Triangles
These triangles have exactly one obtuse angle, meaning an angle greater than 90 degrees, but less than 180 degrees. The other 2 angles will each be acute.

69. A polygon that has four sides
Quadrilaterals
A polygon that has four sides
Paulette Granger

70. Quadrilateral Objectives
Upon completion of this lesson, students will:
have been introduced to quadrilaterals and their properties.
have learned the terminology used with quadrilaterals.
have practiced creating particular quadrilaterals based on specific characteristics of the quadrilaterals.

71. Parallelogram
                                           
A quadrilateral that contains two pairs of parallel sides

72. Rectangle
A parallelogram with four right angles

73. Square
A parallelogram with four congruent sides and four right angles

74. Group Activity
Each group design a different quadrilateral and prove that its creation fits the desired characteristics of the specified quadrilateral. The groups could then show the class what they created and how they showed that the desired characteristics were present.

75. Classifying Angles Dorothy J. Buchanan--NSHS
Geometry
Classifying Angles
Dorothy J. Buchanan--NSHS

76. Right angle
90°
Straight Angle
180°

77. Examples
Acute angle
35°
Obtuse angle
135°

78. If you look around you, you’ll see angles are everywhere
If you look around you, you’ll see angles are everywhere. Angles are measured in degrees. A degree is a fraction of a circle—there are 360 degrees in a circle, represented like this: 360°.
You can think of a right angle as one-fourth of a circle, which is 360° divided by 4, or 90°.
An obtuse angle measures greater than 90° but less than 180°.

79. Complementary & Supplementary Angles
Olga Cazares
North Shore High School

80. Complementary Angles
Complementary angles are two adjacent angles whose sum is 90°
60 °
30 °
60 ° + 30 ° = 90°

81. Supplementary Angles
Supplementary angles are two adjacent angles whose sum is 180°
120°
60°
120° + 60° = 180°

82. Application
First look at the picture. The angles are complementary angles.
Set up the equation:
12 + x = 180
Solve for x:
x = 168°
12° x

83. Right Angles by Silvester Morris

84. RIGHT ANGLES
RIGHT ANGLES ARE 90 DEGREE
ANGLES.

85. STREET CORNERS HAVE RIGHT ANGLES
SILVESTER MORRIS
NSHS

86. Parallel and Perpendicular Lines by Melissa Arneaud

87. Recall: Equation of a straight line: Y=mX+C Slope of Line = m
Y-Intercept = C

88. Parallel Lines Symbol: “||”
Two lines are parallel if they never meet or touch.
Look at the lines below, do they meet?
Line AB is parallel to Line PQ or AB || PQ

89. Slopes of Parallel Lines
If two lines are parallel then they have the same slope.
Example:
Line 1: y = 2x + 1
Line 2: y = 2x + 6
THINK: What is the slope of line 1?
What is the slope of line 2?
Are these two lines parallel?

90. Perpendicular Lines
Two lines are perpendicular if they intersect each other at 90°.
Look at the two lines below: A D C B
Is AB perpendicular to CD? If the answer is yes, why?

91. Slopes of Perpendicular Lines
The slopes of perpendicular lines are negative reciprocals of each other.
Example:
Line 3: y = 2x + 5
Line 4: y = -1/2 x + 8
THINK: What is the slope of line 3?
What is the slope of line 4?
Are these two lines perpendicular. If so, why?
Show your working.

92. What do you need to know Parallel Lines Perpendicular Lines
Do not intersect.
If two lines are parallel then their slopes are the same.
Perpendicular Lines
Intersect at 90°(right angles).
If two lines are perpendicular then their slopes are negative reciprocals of each other.

93. Questions
Write an equation of a straight line that is parallel to the line y = -1/3 x + 7
State the reason why your line is parallel to that of the line given above.
Write an equation of a straight line that is perpendicular to the line y = 4/5 x + 3.
State the reason why the line you chose is perpendicular to the line given above.

94. Basic Shapes by Wanda Lusk

95. Two Dimensional Length Width
Basic Shapes
Two Dimensional
Length
Width
Three Dimensional
Length
Width
Depth (height)

96. Basic Shapes Two Dimensions
Circle
Triangle
Parallelogram
Square
Rectangle

97. Basic Shapes Two Dimensions
Circle

98. Basic Shapes Two Dimensions
Triangle

99. Basic Shapes Two Dimensions
Square

100. Basic Shapes Two Dimensions
Square
Rectangle

101. Basic Shapes Three Dimensions
Sphere
Cone
Cube
Pyramid
Rectangular Prism

102. Basic Shapes Three Dimensions
Sphere
Cone
Cube
Pyramid
Rectangular Prism