Starting Geometry

By: Maria Maldonado HempsteadThis Journal was started:

January 24, 2011

Point, Line, Plane

• Point: A mark or dot that indicates some space.

• Line: A straight path that extends forever.

• Plane: A flat surface that extends forever…

Point A

For example: A piece of paper, the floor, the ceiling.

Collinear Points, and Coplanar Points

• Collinear Points are points that are on the same line.• Non Collinear:

• Collinear:

• Coplanar Points are points that are on the same plane.

Point A Point B

Coplanar Non-coplanar

Line, Segment, Ray

• A line is a straight path that is infinite. Ex.

A Segment is a piece of a line that will connect 2 points. Ex.

A Ray is a part of a line that starts at an end point and extends forever in one direction.

Ex.

These are all related to each other, they just have different ending points, or don’t have any.

What is an Intersection?

• An Intersection is where lines cross eachother’s path.

•

The big blue points are where the lines all intersect.

Postulate, Axiom, and TheoremPostulate: A postulate is a statement that we accept as true even though

there is no proof. For Example: We know that a straight angle with always have 180 degrees, there for if there is a ray dividing the 2 angles we know that both of their angles will add up to 180 degrees.

Axiom: An Axiom is just a another word for a postulate.

Theorem: A theorem, is actually the opposite of a postulate, it is a theory that has been proved. For Example: The midpoint formula:

(x1+x2)(y1+y2)

2 2

Ruler Postulate The Ruler Postulate can be used to find the length a segment.

Suppose we have “a” and “b” on a number line, the ruler postulate will tell us how to find the length AB. What we would do is subtract the coordinates in any other and take the absolute value.

You can take certain points on the football field and subtract them to find out how much a player ran or how far a ball flew while being in the air.

You can use it to find out how much the temperature has dropped or gone up during the day.

If we know that Central Park begins on 57th street and ends on 111th street we can easily find out how many blocks central park is in total.

Segment Addition Postulate

The easiest way to describe the segment addition postulate is to say, if B is between A and C then,

AB+ BC=AC

If we know that half the total length of Scarface is 85 minutes, we can add another 85 minutes and we know that is the entire length of Scarface.

You can use it to find midpoints and distances between places, and on highways.

If Eavany only has half of the money needed to purchase her favorite Juicy Couture dress and the dress costs 300 dollars, then how much money does Eavany have?

How Do I Find Distance Between Two Points On A Coordinate Plane????!!!

Its SUPER EASY! JUST USE THE DISTANCE FORMULA!D= (x1-x2)^2+(y1-y2)^2HOW EASY IS THAT? (It’s totally NOT that easy)ex.

Your points are: (2, 2) (5,1) (2-5)^2 + (2-1)^2= -3^2 +1^2=-9+1=-8

Congruence and Equality

Congruence is when two things have exactly the same measure. Symbol: = Equality is where two things have the same value. Symbol: ≅

Ex. Something that is congruent, when placed right on top of the pre image will be exactly the same.

Something that is equal is like sort of different.

Ex. Of something Congruent:

Ex of Something equal:

A= 5x

Pythagorean Theorem

The Pythogorean Theorem is the area of the three squares surrounding a right triangle.

The Pythogorean equation is: a^2+b^2=c^2

What is an Angle?

An Angle is the measurement in degrees between 2 intersecting lines.

There are 3 types of angles:

Right angle Acute Angle Obtuse Angle

90 degrees 90 degrees or less 90 degrees or moreYou can measure your angles using a protractor.

Angle Addition Postulate

The angle addition postulate states that the sum of the two interior angles in an angle will add up to the total measurement of the angle (where the two angles are inside)

These angles will add up to 90 degrees

These angles will add up to 180 degrees.

These angles will add up to 360 degrees.

MidpointWhat is a midpoint? How can a midpoint be Midpoint Formula constructed?A midpoint is the A midpoint can be (x1+x2) (y1+y2) Point that marks the Contructed by using a 2 2 Exact middle of a compass. Segment.

Coordinates: (1, 3) (4, 7)1+4=5 /2= 2.5 3+7= 10/2=5x= 2.5 y=5

Angle BisectorWhat is an angle bisector? An angle

bisector is a point in the middle of an angle that splits the angle exactly in half (bisects).

To bisect an angle you need to use a compass.

Adjacent, Vertical, Linear

Adjacent: the two angles that are right next to each other.

Vertical: two angles that are non adjacent.

Linear: a pair of non adjacent angles whose non common sides are opposite rays.

Complementary and Supplementary Angles

Complementary Angles:

Supplementary Angles:

These two angles add up to 90 degrees.

These two angles add up to 180 degrees.

Perimeter and AreaSquare: Perimeter: 4+4+4+4=16 Area: 4x4=16

Rectangle: Perimeter:4+4+8+8=24 Area:4x8=32

Triangle: Perimeter:6+6+5=17 Area:5x8=40/2=20

4

4

8

4

6

5

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Area and Circumference of a Circle

Circumference:2pi*rCircumference:2pi*r

2(pi)*6 2(pi)*3

Area: pi*r^2 Area: pi*r^2pi*6^2pi*3^2

6

6

TransformationsReflection: A reflection is a transformation that is exactly the same on each side of the line.

Rotation: A turn of a shape on its point.

Translation: a transformation in which all the points in a figure

move the same distance, and in the same direction.

Work Cited

• http://www.imdbhttp://juicycouturedeals.com/juicy-couture-outlet-listing/• http://www.google.com/imgres?imgurl=http://www.mpsaz.org/jefferson/staff/tepeterson/math/math_glossary/images/co

ordinate.plane.2.gif&imgrefurl=http://www.mpsaz.org/jefferson/staff/tepeterson/math/math_glossary/&usg=__SOrPiysrGhKsVGm5n1IM0EGEqlA=&h=326&w=327&sz=4&hl=en&start=0&zoom=1&tbnid=aQvd1lwNAOnpOM:&tbnh=150&tbnw=150&ei=RCVQTYGgO8P38AbKu_3WDg&prev=/images%3Fq%3Dsmall%2Bcoordinate%2Bplane%26um%3D1%26hl%3Den%26biw%3D1024%26bih%3D642%26tbs%3Disch:1&um=1&itbs=1&iact=hc&vpx=433&vpy=257&dur=374&hovh=159&hovw=159&tx=122&ty=128&oei=MyVQTePKBYP78AbFxsClDg&esq=6&page=1&ndsp=14&ved=1t:429,r:7,s:0

• http://en.wikipedia.org/wiki/Pythagorean_theorem• http://www.chara.gsu.edu/lab/labs/lab1.html• • http://www.google.com/imgres?imgurl=http://www.clipartpal.com/_thumbs/pd/education/compass_drawing_circle.png&i

mgrefurl=http://www.clipartpal.com/clipart_pd/education/compass1.html&usg=__moC05w7FcX4g0nRXHKBMggOgIbc=&h=400&w=358&sz=21&hl=en&start=0&zoom=1&tbnid=a8By9spC8fQjgM:&tbnh=115&tbnw=103&ei=JIpQTbP0O8mBtgfGnfi1AQ&prev=/images%3Fq%3Dcompass%2Bfor%2Bmath%26um%3D1%26hl%3Den%26biw%3D1024%26bih%3D642%26tbs%3Disch:1&um=1&itbs=1&iact=hc&vpx=773&vpy=300&dur=897&hovh=237&hovw=212&tx=118&ty=165&oei=JIpQTbP0O8mBtgfGnfi1AQ&esq=1&page=1&ndsp=19&ved=1t:429,r:18,s:0

• http://www.expressphotocanvas.co.uk/New-York-City-with-reflection.html• .com/title/tt0086250/• http://www.visitingdc.com/new-york/central-park-picture.asp