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CIRCLES. BASIC TERMS AND FORMULAS Natalee Lloyd. Terms Center Radius Chord Diameter Circumference. Formulas Circumference formula Area formula. Basic Terms and Formulas. Center: The point which all points of the circle are equidistant to. .

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circles

CIRCLES

BASIC TERMS AND FORMULAS

Natalee Lloyd

basic terms and formulas
Terms

Center

Radius

Chord

Diameter

Circumference

Formulas

Circumference formula

Area formula

Basic Terms and Formulas
circumference example

Circumference Example

C = 2r

C = 2(5cm)

C = 10 cm

5 cm

area example
Area Example

A = r2Since d = 14 cm then r = 7cm

A = (7)2

A = 49 cm

14 cm

angles in geometry
Angles in Geometry

Fernando Gonzalez - North Shore High School

intersecting lines
Intersecting Lines
  • Two lines that share

one common point.

Intersecting lines can

form different types of

angles.

complementary angles
Complementary Angles
  • Two angles that

equal 90º

supplementary angles
Supplementary Angles
  • Two angles that equal 180º
corresponding angles
Corresponding Angles
  • Angles that are

vertically identical

they share a common vertex and have a line running through them

geometry

Geometry

Basic Shapes

and examples in everyday life

Richard Briggs

NSHS

geometry17

GEOMETRY

Exterior Angle Sum Theorem

what is the exterior angle sum theorem
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

exterior angle sum theorem
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

linking to other angle concepts
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

geometry21

Geometry

Basic Shapes

and examples in everyday life

Barbara Stephens

NSHS

geometry22

GEOMETRY

Interior Angle Sum Theorem

what is the interior angle sum theorem
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

interior angle sum theorem
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

linking to other angle concepts25
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

geometry26

Geometry

Parallel Lines with a Transversal

Interior and exterior Angles

Vertical Angles

By

Sonya Ortiz

NSHS

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

A

interior and exterior angles
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

vertical angles
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

summary
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.
geometry31

Geometry

Parallelograms

M. Bunquin

NSHS

parallelograms
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
kinds of parallelograms
Kinds of Parallelograms
  • Rectangle
  • Square
  • Rhombus
rectangles
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.
squares
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.
rhombus
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.
geometry37

Geometry

Pythagorean Theorem

Cleveland Broome

NSHS

pythagorean theorem
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

slide39

A right triangle has sides a, b and c.

c

b

a

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

slide40

Calculations:

A2 + B2 = C2

16 + 25 = 41

slide41

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.

geometry43

GEOMETRY

Angle Sum Theorem

By: Marlon Trent

NSHS

triangles
Triangles
  • Find the sum of the angles of a three sided figure.
quadrilaterals
Quadrilaterals
  • Find the sum of the angles of a four sided figure.
pentagons
Pentagons
  • Find the sum of the angles of a five sided figure.
hexagon
Hexagon
  • Find the sum of the angles of a six sided figure.
heptagon
Heptagon
  • Find the sum of the angles of a seven sided figure.
octagon
Octagon
  • Find the sum of the angles of an eight sided figure.
what is the angle sum formula
What is the angle sum formula?
  • Angle Sum=(n-2)180
  • Or
  • Angle Sum=180n-360
slide52
A presentation by

Mary McHaney

a square is rectangle

A SQUARE IS RECTANGLE

QUADRILATERAL DILEMMA

THE SQUARE IS A RECTANGLE

OR

THE RECTANGLE IS A SQUARE

square characteristics
SQUARE Characteristics:
  • Four equal sides
  • Four Right Angles
rectangle characteristics
RECTANGLE Characteristics
  • Opposite sides are equal
  • Four Right Angles
square and rectangle share
Square and Rectangle share
  • Four right angles
  • Opposite sides are equal
slide58
SO
  • A SQUARE IS RECTANGLE
  • A RECTANGLE IS NOT A SQUARE
types of triangles

Types of Triangles

Triangles Are Classified Into 2 Main Categories.

triangles classified by their sides scalene triangles
Triangles Classified by Their SidesScalene Triangles
  • These triangles have all 3 sides of different lengths.
isosceles triangles
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.
equilateral triangles
Equilateral Triangles
  • These triangles have all 3 sides of the same length.
acute triangles

Acute Triangles

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

right triangles

Right Triangles

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

obtuse triangles
ObtuseTriangles

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.

quadrilaterals69

Quadrilaterals

A polygon that has four sides

Paulette Granger

quadrilateral objectives
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.
parallelogram
Parallelogram
  • A quadrilateral that contains two pairs of parallel sides
rectangle
Rectangle
  • A parallelogram with four right angles
square
Square
  • A parallelogram with four congruent sides and four right angles
group activity
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.

geometry75

Geometry

Classifying Angles

Dorothy J. Buchanan--NSHS

slide76

Right angle

90°

Straight Angle

180°

slide77

Acute angle

35°

  • Examples

Obtuse angle

135°

slide78
If you look around you, you’ll see angles are everywhere. Angles are measured in degrees. A degreeis 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°.
complementary supplementary angles

Complementary & Supplementary Angles

Olga Cazares

North Shore High School

complementary angles80
Complementary Angles

Complementary angles are two adjacent angles whose sum is 90°

60 °

30 °

60 ° + 30 ° = 90°

application
First look at the picture. The angles are complementary angles.

Set up the equation:

12 + x = 180

Solve for x:

x = 168°

Application

12°

x

right angles
RIGHT ANGLES
  • RIGHT ANGLES ARE 90 DEGREE
  • ANGLES.
recall
Recall:
  • Equation of a straight line: Y=mX+C
  • Slope of Line = m
  • Y-Intercept = C
parallel lines symbol
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

slopes of parallel lines
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?

perpendicular lines
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?

slopes of perpendicular lines
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.

what do you need to know
Parallel Lines

Do not intersect.

If two lines are parallel then their slopes are thesame.

Perpendicular Lines

Intersect at 90°(right angles).

If two lines are perpendicular then their slopes are negative reciprocals of each other.

What do you need to know
questions
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.

basic shapes

Basic Shapes

Two Dimensional

Length

Width

Three Dimensional

  • Length
  • Width
  • Depth (height)
basic shapes two dimensions

Basic ShapesTwo Dimensions

Circle

Triangle

Parallelogram

Square

Rectangle

basic shapes three dimensions

Basic ShapesThree Dimensions

Sphere

Cone

Cube

Pyramid

Rectangular Prism

basic shapes three dimensions102

Basic ShapesThree Dimensions

Sphere

Cone

Cube

Pyramid

Rectangular Prism