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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 = 2r or C = d
Area Formula: A = r2
Circumference Example
C = 2r
C = 2(5cm)
C = 10 cm5 cm
Area Example
A = r2
Since d = 14 cm then r = 7cm
A = (7)2
A = 49 cm
14 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.
11070
40
70
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.
11664 64
52
116
128
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.
20
80 80100100
160
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.
11070
40
70
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.
11664 64
52
116
128
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.
20
80 80100100
160
80 + 80 + 20 = 180
GeometryParallel Lines with a Transversal
Interior and exterior Angles
Vertical Angles
By
Sonya Ortiz
NSHS
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 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 23 4
5 67 8
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 23 45 67 8
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.
D
A 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.
b
a
c
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 Hypotenuseof the right triangle.
The theorem will help calculate distance when travelingbetween two destinations.
GEOMETRY
Angle Sum Theorem
By: Marlon Trent
NSHS
Triangles Find the sum of the
angles of a three 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 ChartName of figure Number of
sidesSum of angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Decagon
n-agon
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 sidesFour 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
Triangles Classified by Their Sides
Scalene Triangles
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.
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.
Paulette Granger
Quadrilaterals
A polygon that has four sides
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 angle90°
Straight Angle180°
Examples
Acute angle35°
Obtuse angle135°
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°.
Complementary & Supplementary
Angles
Olga Cazares
North Shore High School
Complementary AnglesComplementary
angles are two adjacent angles whose sum is 90°
30 °
60 °
60 ° + 30 ° = 90°
Supplementary AnglesSupplementary
angles are two adjacent angles whose sum is 180°120°
60°
120° + 60° = 180°
ApplicationFirst look at the picture.
The angles are complementary angles.
Set up the equation:
12 + x = 180
Solve for x:
x = 168°
12°
x
Right Anglesby
Silvester Morris
RIGHT ANGLES RIGHT ANGLES
ARE 90 DEGREE ANGLES.
STREET CORNERS HAVE RIGHT ANGLES
SILVESTER MORRIS NSHS
Parallel and Perpendicular Lines
byMelissa 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
BC
D
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 + 5Line 4: y = -1/2 x + 8THINK: 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 knowParallel 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.
Questions1. 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.
2. 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 Shapesby
Wanda Lusk
Basic Shapes
Two Dimensional•Length•Width
Three Dimensional•Length•Width•Depth (height)
Basic ShapesTwo Dimensions
•Circle•Triangle•Parallelogram
• Square• Rectangle
Basic ShapesTwo Dimensions
•Circle
Basic ShapesTwo Dimensions
•Triangle
Basic ShapesTwo Dimensions
•Square
Basic ShapesTwo Dimensions
•Square•Rectangle
Basic ShapesThree Dimensions
•Sphere•Cone•Cube•Pyramid•Rectangular Prism
Basic ShapesThree Dimensions
•Sphere•Cone•Cube•Pyramid•Rectangular Prism
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