Geometry Journal

2By Michelle Habie

Conditional statement is formed by a hypothesis and a conclusion. It can be

written in the form: If P then Q.

Parts: If: hypothesis then: conclusion

Conditional Statement:

a. If I study geometry then I will pass the test.

b. If the sky is cloudy then it will rain today.

c. If I finish my homework then I’m able to watch t.v.

Counter example: is an example that proves that a conjecture is false.

No mammals can fly. A bat is a mammal.Three points are allways collinear. Three

points lay on the same plane but only two of them are collinear.

All prime numbers are odd.2 is a prime number.

Counter Example:

Definition and Perpendicular Lines:

It is a concept written in the form of a bi conditional statement to describe a matematical object.

Perpendicular lines are lines that intersect each other forming a 90 degree angle.

A line is perpendicular to a plane at a point.The floor of my house to the walls.The needles of a clock when they matk 3 o’clockThe trash holder is an example of a line

perpendicular to a plane.

Bi- Conditional Statement:A bi conditional statement is a statement that

can be written in the form of P if and only if Q.

They are used to write mathemathical definitions.

They are important to use in our mathematical language and everyday life.

An angle is right IFF it measures 90 degrees.A triangle is acute IFF the 3 angles are acute.3x+1=25 IFF 3=8

Deductive Reasoning:Deductive reasoning uses logic to find a conclusion using facts.We use deductive reasoning to apply the law of detachment and the

law of syllogism.It is used to represent a definition using symbols for a better

understanding.It works making it simpler to understand.If I get on a diet the I will loose weight.If I’m 18 years old then I will get an ID.If I get an ID then I’ll be able to vote.If i’m 18 years old then I’ll be able to vote.If I practice reading then my vocabulary skills will be improven.Symbollic Notation: It is used to represent a definition using symbols for a better

understanding.It works making it simpler to understand.

Laws of Logic:Law of Detachment:If p q is true and p is true it follows that q is also

true.Law of Syllogism:If p q and q r are true it follows that p r is also true.Examples:If I am 16 years old then I can get my drivers license.If I have a blackberry then I am able to chat with people who have bb.If I chat

with people with bb then I will keep in touch with my friends.If two angle measure 45° then they are congruent. If two angles are congruent

then they measure the same.

Algebraic Proof:An algebraic proof is an argument that

uses logic, definitions, properties and proven statements to prove that a conclusion is true.

a. 3x-2=7 Given c. X=2 Given+2 +2 Addition Prop. of Equality 4 Multiplication Prop of Equality3x=9 Division Prop. Of Equality x=8 Simplify 3 3 Simplify x= 3

b. 3r= -12 Given3 3 Diviion Prop. Of Equalityr=-4 Simplify

Segment Prop. of Equality The Segment Addition Postulate states that the sum of the pieces that make up a segment is the same as the length of the whole segment. The same property works for and angle that is divided into two or more parts. The sum of all the parts is the same as the whole angle.

HomeVista Herm. CAG

Examples:

a c eAC+ CE= AEGuate Palin Escuintla Puerto

G-P= G-P+P-E+E-P

Home-CAG= Home-VH+ VH-CAG

Two- column Proof:A two-column proof is written using statements on the left and a

specific reason for each statement in order to find a conclusion to prove what is being asked with a process.

Examples:

Segment Properties of Congruence:Reflexive: Segment AB is only equal to AB. (itself).Symmetric: No matter how we name a segment it is

equal to itself. (AB=BA)Transitive: If AB=BC and BC=CD then AB=CD.Examples:

Home-CAG=CAG-Home

Carlos Luis Pablo

C=lL=P then, C= P is that they are the same in length or height.(Transitive Prop). Laura Me Monica

Laura’s BB= My BBMy BB= Monica’s BBLaura’s= Monica’s BB

Home CAG

Angle Properties of Congruence:Reflexive: <BAC congruent <BAC.Symmetric: <BAC congruent <CAB.Transitive: If <XAW congruent <YAW , <YAW congruent <WAZ

then <XAY congruent <WAZ.

Examples:1.

3.

B

A

C<ABC congruent <ABC

2.B

A

C

D

FE

M

NO

<ABC congruent <DEF ,<DEF congruent <MNO, and <ABC congruent <MNO.

X

Y

Z

<XYZ congruent <ZYX

Linear Pair Postulate:It is made up of two adjacent angles that share a

ray and are supplementary.Examples:

1.

2.A B D

C

X60

ABC and CBD are linear pair then x+ 60= 180°X= 120°

100 X+10

X+10+ 100= 180°X+110=180°X=180-110X=70° 3.

A B

C

D

ACB+ BCD= 180ACB and BCD are linear pair.

Congruent Supplements Theorem:

If two angles are supplements of the same angle then the two angles are congruent.

Examples:1.

2.

AB

C

D

Y

X Z

<CBD is a supplement to <ABC and <YXZ is also a supplement to <ABC SO, <CBD and <YXZ are congruent.

<1

70°

<2 <3

110°70°

<1 is supp to <3<2 is supp to <3So, <1 is congruent to <2.

3. <a <b

< c

If <a is supp to <c Then <b is also supp to <c.

Vertical Angles:Vertical angles are formed whentwo

lines cross and the opposite angles are vertical and congruent. In vertical angles opposite ones (across each other) measure the same.

Examples:

2

3

4

1

<1 and <3 are vertical.

a

a

a

a

X-5

100

If <a and <c are vertical then X-5 + 100 X= 100+5X=105

X+16

2x-6

X+16= 2x-616+6= 2x-x22+x

Bibliography:http://3.bp.blogspot.com/_eIwxugTIJsw/SOUquUJShJI/AAAAAAAAATA/aLgWrMd6o3A/s400/3.3b.bmphttp://www.utdanacenter.org/mathtoolkit/images/activities/geo_b3b_table.gifhttp://mrpilarski.files.wordpress.com/2009/09/proof-in-algebra-pilarski.jpg?w=417&h=333