crescitelli - edtech 506 - reference guide
TRANSCRIPT
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2010 John Crescitelli - Boise State University
1Lines and
Angles
This guide begins the unit. It looks
at types of lines and how those dif-
ferent lines create angles.
2 UnderstandingAnglesPage two examines different types
of angles and teaches how to prop-
erly use a protractor.
3Polygons and
Circles
Page three looks at the differences
between polygons and circles and
defines common terms.
4 Triangles115
30
35
9 9
5
Page four looks at the two ways
that triangles can be categorized
by their sides and by their angles.
5 QuadrilateralsPage five looks at the two ways that
quadrilaterals can be categorized
by parallel sides and congruence.
6Quadrilateral
Venn Diagram
Page six compares and contrasts
the different types of quadrilaterals
in the form of a Venn Diagram.
C=d(pi)=3.1
48 Unit Overview
Page eight is a unit overview. It de-
fines all important terms and shows
important formulas.
7Understanding
Transversals
Page seven explores transversals
and how intersections create
angles with special properties.
130
130
130
130
50
50
50
50
Two Dimensional
Geometry
Unit
Reference
Guide
As we progress through the unit, you will receive the following eight reference guides. Keep them in the
math section of your binder, and organize them in this order. We will reference them in class often.
A Study in Lines, Angles, Polygons, and Circles
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Lines
2010 John Crescitelli - Boise State University
A look at Lines and Angles
Two Dimensional Geometry
Segment
Ray
Line
Angles
Intersecting: Lines, rays, orsegments that pass through
the same point
Perpendicular: Two lines,rays, or segments that cross
at right angles
Parallel: Two lines that donot intersect
90
Line: A figure that extends forever in bothdirectionsRay: Part of a line that has one endpoint andextends forever in the other direction
Segment: Part of a line, with two endpoints
Acute Angle: An anglesmaller than 90
Obtuse Angle: An anglelarger than 90 and smallerthan 180
Right Angle: A 90 angle90
What is an angle anyway?An angle is the space between two rays when
they are connected at their end points. The
common end point the two rays share is
called the vertex.
Vertex
The angle isbetween these
two rays
Reference
Guide 1
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Reference
Guide 2
More on Angles
2010 John Crescitelli - Boise State University
Using a Protractor
A look at Angles and Protractors
Understanding Angles
How to use a Protractor
Place the protractor so that the middle of the zero line is over the vertex, and one side is
over one side of the angle.
Read the pair of numbers where the other side of the angle passes through the protractor.
If the angle is acute, use the smaller number. If the angle is obtuse, use the larger num-ber.
Place the vertex here One ray on the zero line
Read the numbers
that the ray
passes through
Complementary Angles: Two anglesthat add up to 90 (60+30=90)
3060
Supplementary Angles: Two angles thatadd up to 180 (50+130=180)
50 130
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Polygons
2010 John Crescitelli - Boise State University
Circles
A look at Polygons and Circles
Two Dimensional Shapes
Pi: The relationship between the circumferenceand the diameter. = 3.14Circle Formulas= Circumference (c) Diameter (d)Circumference (c) = x Diameter (d)
Pentagon
5 sides
Quadrilateral 4 sides
Quadrilaterals(quad = 4 lateral = side)Refer to your Quadrilateral Venn
Diagram for more information.
Isosceles Right ScaleneEquilateral
Circumference: The perimeter of a circleDiameter: A line connecting two points on a circleand passing through the circles center
Radius: A line from the center of a circle to anypoint on the circles perimeter (radius x 2 = diameter)Diameter (d)
Radius (r)
Circumference (c)
What is a polygon?A polygon is a closed shape madeof connected line segments.
Line segments
connected at
their endpoints
Triangle 3 sides
There are many special polygons
Other polygons to know
cd=C= d
Regular Polygon: A polygon isconsidered regular if all the sides
are the same length and all theangles have the same measure.
The sides of this
triangle are all
equal and so are
the angles.
Congruent: means equal. Thered lines are used to show that the
sides are equal.
Hexagon
6 sides
Octagon
8 sides
Reference
Guide 3
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Angles in a Triangle
2010 John Crescitelli - Boise State University
Sides of a Triangle
A look at triangles and their properties
Exploring Triangles
What makes a triangle a triangle?A triangle is a closed figure made from
three line segments.
Triangles can be classified by the types of angles they have.
Acute: An acute trianglehas three acute angles.
(70+70+40=180)
Line segments
connected at
their endpoints
Right: A right triangle hasexactly one right angle.
(40+90+50=180)
Obtuse: An obtuse trian-gle has one obtuse angle.
(30+115+35=180)
70 70
40
Equilateral: An equilat-eral triangle has three
sides of equal length.
Isosceles: An isoscelestriangle has two sides of
equal length.
Scalene: A scalene trian-gle has no sides of equal
length.
115
30
35
Triangles can also be classified by the types of sides they have.
The sum of the angles of any triangle is always equal to 180.
The red lines mean that those sides are congruent.Congruent: Equal in value. Sides or angles that are of equal measure are calledcongruent.
40
5090
9 97
7
7
5
108
6
Reference
Guide 4
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Parallel Sides on a Quadrilateral
2010 John Crescitelli - Boise State University
Specialized Parallelograms
A look at quadrilaterals and their special properties
Exploring Quadrilaterals
What makes a quadrilateral a
quadrilateral?
A quadrilateral is a closed figure madefrom four line segments.
Quadrilaterals can be classified by the number of parallel sides they have.
Trapezoid: A quadrilateralwith one pair of parallel sides
Line segments
connected attheir endpoints
Parallelogram: A quadrilateralwith two pairs of parallel sides
Rectangle: A parallelo-gram with four congruent
right angles
Rhombus: A parallelo-gram with four sides of
equal length
Square: A parallelogramwith four sides of equal
length and 4 right angles
Parallelograms can also be classified by the types of sides and angles they have.
The red lines mean that those sides or angles are congruent.Congruent: Equal in value. Sides or angles that are of equal measure are calledcongruent.
= This symbol means two lines are Parallel
90
90 90
90 66
66
8
8
8 890 90
90 90
Reference
Guide 5
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Quadr i la tera lsAllquadrilateralsare4sidedpolygons
Trapezoid
Theonlyquadrilateralwith
onesetofparallelsides
Square
Re
Rhombu
Paral le
Aparallelogr
4congruents
4congruenta
Aparallelogram
4congruentsid
Apar
with
angle
Aquadrilateral
with2setsof
parallelsides
2010 JohnT.Crescitelli BoiseStateUniversity
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2010 John Crescitelli - Boise State University
Parallel Lines Crossed by a Transversal
A look at angles created across parallel lines
Understanding Transversals
What is a transversal, anyway?
When two parallel lines are intersected by
another line, that intersecting line is calleda transversal.
The transversal intersects the parallel lines
at exactly the same angle. This creates
relationships between the parallel lines and
the angles in the two intersections.
Those relationships deal with Adjacent,Corresponding and Opposite angles.
Adjacent Angles: Angles that share acommon side are adjacent. In an
intersection, any two adjacent
angles are always supplementary,
or equal to 180.(130 + 50 = 180)
Opposite Angles: Oppositeangles are congruent because
they share the same
supplementary angle.
Corresponding Angles: Anglesthat share the same location in
the intersection with the trans-
versal are corresponding. These
angles are congruent because
the same angle is created.
Reference
Guide 7
The diagonal line is the
transversal of the two
parallel lines.
Parallel
Lines
130 50
13050
130
130
50
50
Congruent: Equal in value. Sides or angles that are of equal measure are calledcongruent.
Adjacent angles are Supplementary. Corresponding and Opposite angles areCongruent.
Remember that a dash
means that the angles
are congruent.
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Lines and Angles Unit Terms
2010 John Crescitelli - Boise State University
Polygons and Circles
A look at Lines, Angles, Polygons, and Circles
Two Dimensional Geometry
Intersecting ParallelPerpendicular
Segment
Ray
Line
LinesLine: A one-dimensional figure thatextends forever in both directionsRay: A part of a line that has one end-point and extends forever in the other
directionSegment: Part of a line, with two end-pointsIntersecting: Lines, rays, or segmentsthat pass through the same pointPerpendicular: Two lines, rays, or seg-ments that cross at right anglesParallel: Two lines that are in the sameplane but do not intersect
AnglesAngle: Two rays with a common end-pointVertex: The common endpoint of tworays, forming an angleAcute: An angle smaller than 90 Right: A 90 angleObtuse: An angle larger than 90 andsmaller than 180Complementary: Two angles whosemeasures add up to 90Supplementary: Two angles whosemeasures add up to 180
PolygonsPolygon: A closed shape whose sidesare formed by line segments.Regular Polygon: All sides are thesame length and all angles have the
same measureCircles
Radius: A line from the center of acircle to any point on the circlesPerimeter (radius x 2 = diameter)Diameter: A line connecting two pointson a circle and passing through the
circles centerCircumference: The perimeter of acirclePi: The ratio of the circumference tothe diameter. Because the ratio never
changes, it is a mathematical con-
stant. The Greek symbol represents
pi, and is equal to 3.14
Right ObtuseAcute
Vertex
Using a Protractor Place the protractor so that the
middle of the zero line is over the
vertex, and one side is over one
side of the angle.
Read the pair of numbers where
the other side of the angle passes
through the protractor.
If the angle is acute, use the
smaller number. If the angle is
obtuse, use the larger number.
Triangle 3 sides
Pentagon
5 sides
Hexagon
6 sides
Octagon
8 sides
Quadrilateral
4 sides
QuadrilateralsRefer to your Quadrilateral Venn
Diagram for more information.
Isosceles Right Scalene
(pi)= 3.14
Diameter (d)
Radius (r)
Circumference (c)
cd=Circle Formulas
= Circumference(c) Diameter(d)Circumference(c) =x Diameter(d)
C= d
Equilateral
Reference
Guide 8