How do we find the area of a circle?

Area=pi.r.r 
                                                                                             A=pi.5.5
                                                              25pi
                                                                                                   

How do we calculate the surface area of a cylinder?

   SA(cylinder)= LA + 2B
                           LA= 2pi.r.h
                                    2B= 2(area of base)
                                            2(pi.r.r)

               LA= 2pi.r.h    +    2B= 2(pi.r.r)
                   2pi.3.6                 2(pi.3.3)

                   2pi.18                  2(pi.9)

                   36pi           +        18pi   

                              SA=54pi                                   

How do we use conjuctions and disjunctions?

Conjuctions-Hooking up words and phrases and clauses with AND. A conjuction has two statements connected by and. A conjuction is true when both parts are true otherwise it is false.
    
              Ex. Mary is on the softball team and Rob is on the football                        team.
                
Disjuctions-Hooking up words and phrases and clauses with OR. Two statements connected by or.A disjunction is false when both are false otherwise it is true.
     
             Ex. Mary is on the softball team or Rob is on the football team.

How Do We Do Compositions of Transformation?

Composition of Transformations-When two or more transformations are combined to form a new transformation , the result is called a composition of transformation 

Example:  (2,6)

Always do second transformation first

First reflect (2,6) over the x-axis.
    x-axis (x,y)---(x,-y)
              (2,6)---(2,-6)

Second dilation by multiplying by 2 in both x and y
     2 multiplied by 2= 4  x=4
    -6 multiplied by 2=-12 y=-12
                    (4,-12)

Final answer=(4,-12)

What are the special Parallelograms?

A rhombus is a parallelogram with four congruent sides.

 The diagonals of a rhombus are perpendicular. The diagonals bisect the angles and bisect each other.

A rectangle is a parallelogram with four congruent angles, or an 

"equiangular parallelogram". The diagonals of a rectangle are congruent and bisect each other. 

A square is a equilateral rectangle. A squares diagonal are congruent,  perpendicular and they bisect each other.

What are properties of kites?

Kite

• Two pairs of consecutive congruent sides
• Diagonals are perpendicular
• The vertex diagonal Bisect the other diagonals
• The vertex diagonal is an angle bisector of the vertex angles

       

How can we prove that triangles are congruent?

Two Triangles- are congruent if and only if all their corresponding sides and angles are congruent.

Side-Side-Side Triangle Postulate (SSS)- If 3 sides of a triangle are congruent to 3 sides of another triangle then the two triangles are congruent. 
Triangles ABC=XYZ

Side-Angle-Side Triangle Postulate (SAS)- If 2 sides of a triangle and the included angle are congruent to the 2 sides of another triangle and its included angle , 
then the two triangles are congruent.Triangles ABC=XYZ

Angle-Side-Angle (ASA)- triangles are congruent if any two angles and their included side are equal in both triangles.
Triangles ABC=XYZ


Angle-Angle-Side congruence Postulate (AAS)- Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangle.
Triangle ABC=XYZ

How do we use the exterior angle thereom?

The measures of an exterior angle in a triangle is equal to the sum of the measurements of the two remote interior angles.


                         Example- <x=50              
                                                              <y=80    
                                          50+80=130
                                                                <z = 130

How do we use the triangle sum conjecture?

Triangle sum conjecture- the sum of the measures of the angles in                                                             every triangle.

Conjecture-the sum of the measures of the angles in every triangle is 180.

Example-  55+80+45= 180 
or if you didn't have all the angles like 45 you do this
                  80+55=135
                  180-135=45

What are the special angles we can create with parallel lines?

                                  

Transverse- a line that intersects two or more other coplanar lines.

Corresponding angles- angles that are in the same position relative to the transverse and lines.<1=<5 ,<2=<6, <3=<7 ,<4=<8

Corresponding angles conjecture- if two parallel lines are cut by a transverse then corresponding angles are congruent.
<1=<5 ,<2=<6, <3=<7 ,<4=<8

Alternate interior angles conjecture-if two parallel lines are cut by a transverse ,then alternate interior angles are congruent.
<3=<6, <4=<5

Alternate exterior angles conjecture- they are congruent
<3=<6, <4=<5

Consecutive interior/exterior angles conjecture - they are supplementary <1=<8, <2=<7

What are the special segments of triangles?

Altitude- the height of a triangle.      




Angle Bisector-Bisects an angle in half, creating two congruent angles.

Median-connects the vertex of an angle to the midpoint of the opposite side.

What are the basic building blocks of geometry?

Point-a point specifies only location. It has no length ,width, or depth.We usually represent a point with a dot on paper and label it and make it have dimensions, while a true points dimension is 0.

Line-a line has only one dimension: length. It contains forever in two directions (so it has infinitive length), but it has no width at all. A line connects two points.






Line segment-a line that has two end points.




Plane-a plane is a flat, two dimensional object.

              Ray-a line with one end point

                     Collinear-a line on the same line



Coplanar-a plane on the same plane

How to calculate the midpoint of a segment?

Midpoint Formula-
        Midpoint as being halfway between two locations.( the mean average)

 Example- (-9,-1) (-3,7)
                                                                                     A= (-9,-1)
                                                                                     B= (-3,7)
                               M= (-6.3)
  

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