What are special parallelograms

Polygon-A four-sided figure with opposite sides parallel.

Special Parallelograms include shapes such as:

Rhombus

• The diagonals are perpendicular 
• the diagonals bisect the angles
• the diagonal bisect each other

Rectangle

• four congruent angles
• the diagonals are congruent to each other
• the diagonals bisect each other
• opposite sides are congruent

Square

• all sides are congruent
• all angles are congruent
• diagonals are perpendicular
• diagonals are congruent

How do we define circles?

Circle-a simple shape of Euclidean geometry that is the set of all points in a plane that are a given distance from a given point, the center. The distance between any of the points and the center is called the radius. the degrees of a circle equal 360.
Parts of a circle include the center, radius, circumference, diameter, a chord, and a tangent.


Center- the spot in which all medians of a circle meet.
Radius- the distance between the center of a circle to the edges of the circle
Diameter- any straight line segment that passes through the center of the circle or sphere and whose endpoints lie on the circle or sphere. It can be also defined as the longest chord of the circle or sphere.

Chord-a geometric line segment whose endpoints both lie on the circle.


Tangent-A line that touches a circle in exactly one point

What are congruence shortcuts.

Side-Angle-Side Triangle Postulate
The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.



if two sides of the triangles are congruent, and one pair of angles are congruent then the two triangles are congruent.

Angle-Side-Angle Congruence Postulate
The Angle Side Angle postulate (often abbreviated as ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then these two triangles are congruent.


if two pairs of angles are congruent and on pair of sides are congruent in two triangles, then the triangles are congruent

How to calculate midpoint of a line segment

Midpoint- the point that is the same distance from the two endpoints on a line segment



Example:
Find the midpoint of a Line segment  connecting points (6,4) and (3,-4)

6+3 , 4+(-4)   

  2      2

[(9/2),(0/2)]

Midpoint= (4.5,0)