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CIRCLES
BASIC TERMS AND
FORMULAS
Natalee Lloyd
Basic Terms and
Formulas
Terms
 Center
 Radius
 Chord
 Diameter
 Circumference
Formulas
 Circumference
formula
 Area formula
Center: The point which all
points of the circle are
equidistant to.
Radius: The distance from
the center to a point on
the circle
Chord: A segment
connecting two points on
the circle.
Diameter: A chord that
passes through the center
of the circle.
Circumference: The
distance around a circle.
Circumference Formula:
C = 2r or C = d
Area Formula:
A = r2
Circumference Example
5 cm
C = 2r
C = 2(5cm)
C = 10 cm
Area Example
14 cm
A = r2
Since d = 14 cm
then r = 7cm
A = (7)2
A = 49 cm
Angles in Geometry
Fernando Gonzalez - North Shore High School
Intersecting Lines

Two lines that share
one common point.
Intersecting lines
can
form different types
of
angles.
Complementary Angles

Two angles that
equal 90º
Supplementary Angles

Two angles that equal 180º
Corresponding Angles

Angles that are
vertically identical
they share a
common vertex and
have a line running
through them
Geometry
Basic Shapes
and examples in everyday life
Richard Briggs
NSHS
GEOMETRY
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

There are 3 exterior
angles in a triangle.
The exterior angle
sum theorem applies
to all exterior angles.
128
52
64
116
64 116
128 = 64 + 64 and 116 = 52 + 64
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
Geometry
Basic Shapes
and examples in everyday life
Barbara Stephens
NSHS
GEOMETRY
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

There are 3 interior
angles in a triangle.
The interior angle
sum theorem applies
to all interior angles.
128
52
64
116
64 116
128 = 64 + 64 and 116 = 52 + 64
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 + 80 + 20 = 180
80
100
Geometry
Parallel Lines with a Transversal
Interior and exterior Angles
Vertical Angles
By
Sonya Ortiz
NSHS
Transversal



A
Definition:
A transversal is a
line that intersects a
set of parallel lines.
Line A is the
transversal
Interior and Exterior
Angles

1 2
3 4
5
6
7 8



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
Vertical Angles

1 2
3 4
5
7 86





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
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.
Geometry
Parallelograms
M. Bunquin
NSHS
Parallelograms

A parallelogram is a a special
quadrilateral whose opposite sides are
congruent and parallel.
A
D
B
C
Quadrilateral ABCD is a parallelogram if and only if
1. AB and DC are both congruent and parallel
2. AD and BC are both congruent and parallel
Kinds of
Parallelograms

Rectangle

Square

Rhombus
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







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






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.
Geometry
Pythagorean Theorem
Cleveland Broome
NSHS
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

A right triangle has sides a, b and c.
c
b
a
If a =4 and b=5 then what is c?
Calculations:
A2 + B2 = C2
16 + 25 = 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.
The theorem will help calculate distance when traveling
between two destinations.
GEOMETRY
Angle Sum Theorem
By: Marlon Trent
NSHS
Triangles

Find the sum of the
angles of a three
sided figure.
Quadrilaterals

Find the sum of the
angles of a four
sided figure.
Pentagons

Find the sum of the
angles of a five
sided figure.
Hexagon

Find the sum of the
angles of a six
sided figure.
Heptagon

Find the sum of the
angles of a seven
sided figure.
Octagon

Find the sum of the
angles of an eight
sided figure.
Complete The Chart
Name of figure Number of
sides
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Decagon
n-agon
Sum of angles
What is the angle sum
formula?
Angle Sum=(n-2)180
 Or
 Angle Sum=180n-360

A presentation by
A SQUARE IS RECTANGLE
THE SQUARE IS A RECTANGLE
OR
THE RECTANGLE IS A SQUARE
SQUARE
Characteristics:
Four
equal sides
Four Right Angles
RECTANGLE Characteristics
Opposite sides are equal
 Four Right Angles

Square and Rectangle
share
 Four right angles
 Opposite sides are equal
SQUARE AND RECTANGLE
DO NOT SHARE:

All sides are equal
SO


A SQUARE IS RECTANGLE
A RECTANGLE IS NOT A SQUARE
Charles Upchurch
Types of Triangles
Triangles Are Classified Into 2
Main Categories.
Triangles Classified
by Sides

These triangles have all 3 sides of
different lengths.
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

These triangles have all 3 sides of the
same length.
Triangles
Classified by
their Angles
Acute Triangles
These Triangles Have All Three
Angles That Each Measure Less
Than 90 Degrees.
Right Triangles
These triangles have exactly one
angle that measures 90 degrees.
The other 2 angles will each be
acute.
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.
Quadrilaterals
A polygon that has four sides
Paulette Granger
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
• A quadrilateral that
contains two pairs
of parallel sides
Rectangle
• A parallelogram with
four right angles
Square
• A parallelogram with
four congruent sides
and four right
angles
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.
Geometry
Classifying Angles
Dorothy J. Buchanan--NSHS
Right angle
90°
Straight Angle
180°

Examples
Acute angle
35°
Obtuse angle
135°
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 onefourth 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
Olga Cazares
North Shore High School
Complementary Angles
Complementary
angles are two
adjacent angles
whose sum is 90°
60 °
30 °
60 ° + 30 ° = 90°
Supplementary Angles
120°
60°
120° + 60° = 180°
Supplementary
angles are two
adjacent angles
whose sum is 180°
Application
12°
x
First look at the
picture. The angles
are complementary
angles.
Set up the equation:
12 + x = 180
Solve for x:
x = 168°
Right Angles
by
Silvester Morris
RIGHT ANGLES


RIGHT ANGLES
ARE 90 DEGREE
ANGLES.
STREET CORNERS
HAVE RIGHT ANGLES
SILVESTER MORRIS
NSHS
Parallel and
Perpendicular Lines
by
Melissa Arneaud
Recall:
Equation of a straight line: Y=mX+C
 Slope of Line = m
 Y-Intercept = C

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
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
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
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
1. Do not intersect.
2. If two lines are
parallel then their
slopes are the
same.
Perpendicular Lines
1. Intersect at
90°(right angles).
2. If two lines are
perpendicular then
their slopes are
negative
reciprocals of each
other.
Questions
1.
2.
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
by
Wanda Lusk
Basic Shapes
Two Dimensional
•Length
•Width
Three Dimensional
•Length
•Width
•Depth (height)
Basic Shapes
Two Dimensions
•Circle
•Triangle
•Parallelogram
• Square
• Rectangle
Basic Shapes
Two Dimensions
•Circle
Basic Shapes
Two Dimensions
•Triangle
Basic Shapes
Two Dimensions
•Square
Basic Shapes
Two Dimensions
•Square
•Rectangle
Basic Shapes
Three Dimensions
•Sphere
•Cone
•Cube
•Pyramid
•Rectangular
Prism
Basic Shapes
Three Dimensions
•Sphere
•Cone
•Cube
•Pyramid
•Rectangular
Prism