Crescitelli - EdTech 506 - Reference Guide

8/7/2019 Crescitelli - EdTech 506 - Reference Guide

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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


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


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


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


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


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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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


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

Documents

Crescitelli - EdTech 506 - Reference Guide