Geometry JournalMichelle Habie 9-3

Point, Line, PlanePoint: A mark or dot that indicates a location.Ex: Line: A straight collection of dots that go on forever.Ex: Plane: Flat surface that extends forever.Ex:

Collinear Points & Coplanar Points:

Collinear Points:Points that are in the same line. Ex:Non collinear Points:Points that are not in the same line.Ex:

Coplanar Points: Points that are on the same plane.Ex:

This is an example of coplanar points that are not collinear.

This 3 points are coplanar and collinear.

Line, Segment, RayLine: A straight collection of dots that go on forever.Ex:Segment: A line that has a beginning and an end.Ex:Ray: A line that has a starting point and in one side it keeps on going forever and in the other side, it stops.Ex:

The three of them join two points however, some stop and other continues their path.

What is an intersection?Intersection:

The point where a line crosses the x axis or the y axis. Passing across each other at exactly one point.

Exmples:1. 2. 3.

Real Life Intersection

Postulate, Axiom, Theorem:Difference:

Postulate:A statement that is accepted as true without proof.

Axiom:A statement that is accepted as true without proof.

Theorem:A statement that has been proven.

Ruler Postulate: To measure any segment you use a ruler and

subtract the values at the end points.

Examples: 1. 2.

3.

5 8

BA

Base 2

Base

1

Use the ruler postulate to find the distance from one point to the other.

Segment Addition Postulate:If A,B and C are 3 collinear points and B is between A and C then AB+BC=AC.

Examples:A CB

1 2 3

CAGVista

Hermosa

Blvd.

Home

Use this postulate to find the distant between 3 or more points on a segment.

Distance between 2 points:To find the distance between two points you use the distance formula:√(x2-x1)⌃2+(y2-y1)⌃2

Examples:1. (2,4) (-1,0)D=√(2+1)⌃2+(4-0)⌃2=D=52. (3,-2) (6,-8)D=√(3-6)⌃2+(-2+8)⌃2=D=√453. (1,0) (-2,8)D=√(1=2)⌃2+(0-8)⌃2=D=√73

Congruent – Equal:≅ Two things that have equal measure.Might not know what the value is.Comparing Names.

--≅--AB CD

=Two things that have the same value.We have to know the valueComparing ValuesAB=3.2

Examples:

BA C

A, B are congruent and equal.While B, C are congruent but, not equal.

Pythagorean Theorem: The sum of the legs to the squared has to be equal to the hipothenuse to the square.

Examples:a2+ b2=c2

If a=10 and b=12Find c:c=√(102)+(122)C=√244

Find aA=√10⌃2-8⌃2A=√100-64A=√36=6

A=10 c=16Find bb=√16⌃2-10⌃2B=√256-100 = b=√156B=8 c=10

Angles and types of angles:An angle is the joining of two rays with a common point called vertex. We measure the angles by the distance from ray to ray, we measure

them in degrees.1. Acute angle (measures 0°-89°)2. Right angle (measures exactly 90°)3. Obtuse angle (measures between 91°-179°)4. Straight angle (measures exactly 180°)

The parts of an angle are its legs and the vertex.

Legs

Legs

Interior

Vertex

Angle addition Postulate:The measurement of two included angles is equal to the measurement of the whole angle that includes both.

<CAD+<CAB=<BAD 1. m<CAD= 30° m<CAB=20°Find m<BADm<BAD=30°+20°=50°

2. m<BAD= 75° and m<CAD= 15° Find m< CABm<CAB=75°-15°=60°

3. <EIF=32°, <FIG=40°, <GIH=38°Find m<EIHm<EIH=32°+40°+38°=110°

A

B

C

D

EF

G

HI

MidpointThe midpoint is the point that bisects a segment in two congruent parts.

You can find a midpoint by measuring or using a straight edge( compass).

Examples:1. A C

is the midpoint Because lies in the middleof segment A,C.

B

E F

If EF= 10 and FG= 9, then F is NOT the midpoint of EG.

G

The apple balances this scale because it represents the midpoint.

Angle Bisector:It means to divide an angle into two congruent angles.

To construct an angle bisector you use a compass and a ruler to find it.

Example 1:

Adjacent,Vertical, Linear Pairs of Angles:

Adjacent: Have a common vertex sharing a ray with no common interior points.

Vertical: Two non adjacent angles form by two intersecting lines.

Linear: Adjacent angles with non common sides are opposite rays.

Supplementary & Complementary Angles:

Supplementary:Any two angles that add up to 180°

Complementary:Any two angles that add up to 90°

Area and Perimeter of Shapes:A= s⌃ 2

P= 4sExample 1 : s=5inA=(5)⌃2=25in ⌃2P=4×5=20in

Example 2: s=3cm A=(3)⌃2=9cm⌃2P=4×3=12 cm

A= l wP= 2l + 2wExample 1 : l= 2 cm, w= 1 cm A = 2×1=2cm ⌃2 P =2(2)+ 2(1)=6cmExample 2:l= 5 ft, w=3ftA= 5×3=15ft⌃2P= 2(5)+ 2(3)= 16ft

A= ½ l hL= a+b+cExample 1 : l= 5, w= 3, b=4, c=6 A = 5×3÷2= 7.5 u ⌃2L = 5+4+6= 15u Example 2:l=7, w=4, b=2, c=5A= 7×4÷2= 14u ⌃2L=7+2+5= 14u

Area and Circumference of a Circle

Area= π r ⌃2

Example 1:r= 6A(3.14)(6)⌃2A=3.14×36A=112.04u⌃2

Circumference: 2π r

Example 1:r= 8cm c= 2(3.14)(8)c= 50.24cm

5 Step Process: If three cans of soda cost $10.50. How much would

seven cans of soda cost?1. Read it carefully.2. Understand the problem3. Make a plan- I definetly need to set up a proportion.4. 3 cans=7 cans

------ = ------ = 10.50 ×710.50 x ------------

3x=$24.50

5. Look Back if the answer makes sense.

Transformations:Make a copy of a figure in a different position. A transformation can enlarge an object or shrink an object.

Examples:

RotateReflectTranslate

Bibliography:• http://primaryhomeworkhelp.co.uk/time/pm.gif• http://gmat4all.com/diagrams/a1a.jpeg• http://www.bced.gov.bc.ca/irp/mathk7/icons/f6.gif• http://www.gogeometry.com/heron/angle_bisector.gif• http://content.tutorvista.com/maths/content/geometry/lines%20angle

s%20triangles/images/img61.gif• http://www.freemathhelp.com/images/lessons/angles5.gif• http://2000clicks.com/MathHelp/GeometryTheoremsLinearPair.gif• http://www.analyzemath.com/Geometry/angle_5.gif• http://www.gltech.org/library/April_geometry/supplementary2.gif• http://image.wistatutor.com/content/feed/tvcs/translation_0.jpg• http://image.wistatutor.com/content/feed/u1856/reflection.GIF• http://www.mathsisfun.com/geometry/images/rotation-2d.gif