Chapter 4

Vocabulary

Acute angles=any angle smaller than 90 degrees
Obtuse angle= any angle larger than 90 degrees
Right angle= 90 degrees
Acute triangle= a triangle with 3 acute angles
Obtuse triangle= a trianle with on obtuse angle
Equiangular triangle=3 congruent acute angles
Right triangle= 1 right angle
Equilateral triangle=a triangle with 3 congruent sides
Isosceles triangle=a triangle with at least 2 congruent sides
Scalene Triangle= No congruent sides

Chapter 3

Vocabulary

Transversal=a line that intersects to coplanar lines at 2 different points
Corresponding angles=Angle that are on the same side as the transversal
Alternate interior angles=angles that are on different sides of the transveral, but are in between the 2 other lines
Alternate exterior angles=Angles that are on different sides of the transversal and are on the opposite sides of the 2 other lines
Same side interior angles= Angles that are on teh same side of the transversal and on teh inside of the 2 other lines

 ----------
  ----------     = Parallel Lines

  |________    = Perpendicular Lines
  |


Proving Lines are Parallel

1.Converse of the alternate interior angles
2.Converse of the alternate exterior angles
3.Converse of the same-side interior angles
4.Converse of the corresponding angles
5.If 2 lines are perpendicular to the same line the they must be parallel         ----------- ^

Finding the Slope

Equation:    y1-y2  =  once you find the answer you divide the top number by the bottom and thast the slope.

                 x1-x2 

    

                5-3 = 2 = 1
                                                                                                 4-2    2

Chapter 2

Vocabulary

Conjectures= "If this, then that" --> If two lines are congruent then they have the same lenth

Biconditional statements- If p->q , and p-> r, then q->r

PROOFS:

Addition Property of Equality = if a=b, then a+c=b+c
Subtraction Property of Equality= if a=b, then a-c=b-c
Multipilication Property of Equality=if a=b,then ac=ab
Division Property of Equality=if a=b, and c (doesnt)=0, then a/c=b/c
Reflexive Property of Equality=a=a
Symmetric Property of Equality= if a=b, then b=a
Trasitive Property of Equality=if a=b and b=c, then a=c
Substitution Property of Equality= if a=b the b can be substituted for a in any expression
Reflexive Property of Congruence=EF=EF
Symmetric Property of Congruence=if <1=<2, then<2=<1
Transitive Property of Congruence=if pq=rs and rs=tu, then pq=tu
Verticle Angles Theorem= <A=<B
Right Angle Congruence Theorem=a and b are right angles, <a=<b
Congruent Complements/Supplements Theorem= ,1 and <2 are complementary/supplemantary, <2 and<3 are complementary/supplementary, <1=<3

Example of a Proof---------->

Chapter 1

Vocabulary

Lines = A strait path the extends forever
Planes=A flat surface the extends forever
Points= A dot that names a location and has no size
Segments= A part of a line consisting of 2 points and can have some points between them
Endpoints= A point at the end of a segment
Rays=A part of a line that starts at an endpoint and extends forever
Opposite Rays= 2 rays that share an end point

To find Collinear points you have to look for points that are on the same -------------------------------------------------------------------->

When finding a midpoint you should use the midpoint formula

M ( x1+x2, y1+y2)
           2    ,     2

When finding the distance between 2 points to use the distance formula

AB = (1-2)2 + (3-4)2 -----Square rooted

Perimeter and Area formulas

Rectangle:
P=2l+2w
A=lw

Square:
P=4S
A=S2

Triangle:
P=a+b+c
A=1/2 BH

Transformation
Reflection= when the image looks reflected (flipped)
Rotaion= When the image is turned (still the same shape but different position)
Translation= when the object is slided into a different direction