1. Geometry
Journal 2
By Michelle Habie

2. Parts: If: hypothesis then: conclusion
Conditional Statement:
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
If I study geometry then I will pass the test.
If the sky is cloudy then it will rain today.
If I finish my homework then I’m able to watch t.v.

3. 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.

4. 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’clock The trash holder is an example of a line perpendicular to a plane.

5. 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

6. 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.

7. 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.

8. Algebraic Proof:
An algebraic proof is an argument that uses logic, definitions, properties and proven statements to prove that a conclusion is true.
3x-2=7 Given c. X=2 Given
Addition Prop. of Equality 4 Multiplication Prop of Equality
3x= Division Prop. Of Equality x=8 Simplify
Simplify
x= 3
b. 3r= Given
3 3 Diviion Prop. Of Equality
r=-4 Simplify

9. 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.
Home Vista Herm. CAG
Examples:
a c e
AC+ CE= AE
Home-CAG= Home-VH+ VH-CAG
G-P= G-P+P-E+E-P
Guate
Palin
Escuintla
Puerto

10. Two- column Proof: Examples:
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:

11. 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
Home
CAG
C=l
L=P then, C= P is that they are the same in length or height.(Transitive Prop).
Laura’s BB= My BB
My BB= Monica’s BB
Laura’s= Monica’s BB
Carlos
Luis
Pablo
Laura Me
Monica

12. 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: X
<XYZ congruent <ZYX Y A D M A Z B E N 2. C F O B
<ABC congruent <DEF ,<DEF congruent <MNO, and <ABC congruent <MNO.
<ABC congruent <ABC C

13. Linear Pair Postulate:
It is made up of two adjacent angles that share a ray and are supplementary.
Examples: 1. 2. C
ABC and CBD are linear pair then x+ 60= 180°
X= 120° 60 X A B D
X = 180°
X+110=180° X=
X=70° B 3. A
100
X+10
ACB+ BCD= 180
ACB and BCD are linear pair. C D

14. Congruent Supplements Theorem:
If two angles are supplements of the same angle then the two angles are congruent. Examples: 1. 2.
<CBD is a supplement to <ABC and <YXZ is also a supplement to <ABC SO, <CBD and <YXZ are congruent. Y C B A D X Z
<1 is supp to <3
<2 is supp to <3
So, <1 is congruent to <2.
110°
70°
70°
<1
<2
<3

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

16. 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:
If <a and <c are vertical then X
X= 100+5
X=105
X-5 2
<1 and <3 are vertical. a 1 3 a a 4 a
100

17. X+16
X+16= 2x-6
16+6= 2x-x
22+x
2x-6

18. Bibliography: