How Do We Use Conjunctions and Disjunctions?

 

 

Conjunctions:

Hooking up words and phrases and clauses with AND.

- Has two statements connected by AND

 

 

Disjunctions:

Hooking up words and phrases and clauses with OR

- Has two statements connected by OR

 

 

Conditional:

The most frequently used statement in the construction or an argument or in the study of mathematics

       -Conditional- "if" (hypothesis), "then" (conclusion)

       - Inverse- Negate "if", "then"

       - Converse- switch "if", "then"

       - Contrapositive- Negate the converse 

How Do We Use Contrapositives?

 

Contrapositives:

Contra- prefix meaning "against" or "opposite"

you negate AND switch the hypothesis and conclusion (inverse and converse)

 

 

Examples:

1. "If I study, then I'll pass geometry." = "If I don't pass geometry, then I didn't study."

     2.  "If I am tired. then I will go to sleep." = "If I don't go to sleep, then I am not tired."

 

The "if" and "then" don't change with the hypothesis and the conclusion.

   

     3. "If Lisa sells the house, than her income will not remain the same." = "If her income does stay the same, then Lisa won't sell the house."

    

    4. "If a number is divisible by six, than it is divisible by three." = "If a number isn't divisible three, then it isn't divisible by six."

how do we use circle equations to solve problems?

How Do We Use Circle Equations to Solve Problems?

What is the midpoint?

(5,2) and (-3,-4)                          -4+2=-2

5+-3=2                                         -2/2=-1

2/2=1                                           -1=y

1=x

m=(1,-1)

What is the distance from (1,-1) to (5,2)?

d= (5-1)^2+ (2+1)^2

d= 16+9

d= 25

d=5

how do we define circles?

How Do We Define Circles?

Circle

A circle is the set of all points in a plane at given distance froma given point.

http://www.math.com/school/subject3/lessons/S3U1L6GL.html

-Given distance is the radius

- point is called the center

Chord

A line segment that connects two points on a circle 

http://en.wikibooks.org/wiki/Geometry/Chapter_7

Diameter

A line segment through the center with endpoints on the circle

http://openhighschoolcourses.org/mod/book/view.php?id=258&chapterid=500

Tangent

A line that touches a circle in exactly one point.

http://www.icoachmath.com/math_dictionary/Common_External_Tangent.html

-Congruent circles have the same radius

-Concentric circles have the same center

Semicircle

half a circle= 180 degrees

Minor Arch- less than 180 degrees

Major Arch- more than 180 degrees

what are the special parallelograms?

What Are The Special Parallelograms?

Rhombus

A parallelogram with four congruent sides.

http://math.tutorvista.com/geometry/quadrilaterals.html



In the example above, the diagonals bisect the angles and they also bisect each other.



Rectangle

Parallelogram with four congruent angles or an "equiangular parallelogram."

http://www.geom.uiuc.edu/~dwiggins/conj28.html

The diagonals of a rectangle are congruent and they bisect each other.

Equilateral Rectangle

Equiangular rhombus

http://quizlet.com/6547298/geometry-terms-cfh-flash-cards/

Diagonals are congruent, perpendicular and they bisect each other.







how do we use the properties of trapezoids?

 

How Do We Use the Properites Of Trapezoids?

 

 

 

Trapezoids

exactly on pair parrallel sides

http://www.kidsmathgamesonline.com/pictures/shapes/trapezoid.html

 



Trapezoid Consecutive Angles Conjecture

the consecutive angles between the bases of a trapezoid are parrallel and have 180 degree supplementary angles

 

 

http://standards.ospi.k12.wa.us/FullGlossary.aspx?subject=7,PE

Isosceles Trapezoid Conjecture

the base angles of an isosceles trapezoid are congruent

 



http://www.geom.uiuc.edu/~dwiggins/conj19.html



what are the properties of kites?

 

 

What Are the Properties Of Kites?

 

 

 

Kite

two pairs of consecutive congruent sides

ex:

http://www.wyzant.com/Help/Math/Geometry/Areas/Rhombuses_and_Kites.aspx

In kite abcd, segment ab is congruent to bc because the angles are adjacent to each other. It's the same with segments ac and dc.

 

 

Properties of Kites

1) the nonvertex angles are congruent

2) diagonals are perpendicualar

3) the vertex diagnal bisects the other diagonal

4) the vertex diagonsl is an angle bisector of the vertex.

 

 

 

 

 

http://emathlab.com/Geometry/Quadrilaterals/TrapezoidsKites.php