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)
  

\