Studied by 2 people
collinear
points that lie on the same line
Coplanar
points that lie on the same plane
perpendicular lines
Lines that intersect to form right angles
skew lines
non parallel, non coplanar (they do not intersect but go in different directions)
midpoint
A point that divides a segment into two congruent segments
segment bisector
either a point, line, ray or other segment that intersects a segment at its midpoint
Midpoint formula on a coordinate plane
(x₁+x₂)/2, (y₁+y₂)/2
midpoint formula on a number line
(a + b)/2
angle
formed by two rays with the same endpoint
rays
a part of a line that has a fixed starting point but no endpoint
vertex
the point shared by both rays
What unit is used to measure angles?
degrees
congruent angles
angles with the same measure
angle bisector
a ray, line, or segment, that splits an angle into two congruent angles
acute angle
less than 90 degrees
rigth angle
90 degrees
obtuse angle
An angle between 90 and 180 degrees
straight angle
an angle that measures 180 degrees
adjacent angles
two coplanar angles with a common side, a common vertex, and no common interior points (no overlap)
vertical angles
two angles whose sides are opposite rays (vertical angles are congruent)
complementary angles
Two angles whose sum is 90 degrees
supplementary angles
Two angles whose sum is 180 degrees
linear pair
a pair of adjacent angles whose non-common sides are opposite rays. the angles of a linear pair form a straight angle (180 degrees) *angles are always supplementary
the distance formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
perpendicular bisector of a segment
a line segment, or ray that is perpendicular to a segment at it's midpoint
perimeter of a square
4s
area of a square
s²
perimeter of a triangle
a+b+c
Area of a triangle
1/2bh
Perimeter of a rectangle
2(b+h)
Area of a rectangle
bh
circmference of a circle
2πr
area of a circle
πr²
inductive reasoning
reasoning based on patterns you observe
conjecture
a conclusion you reach using inductive reasoning
Counter example
a specific example that shows a conjecture is incorrect
conditional
an if-then statement
What is the "if" part of a conditional statement called?
hypothesis
What is the "then" part of a conditional statement called?
conclusion
negation
the negative or opposite of that statment
Inverse
negate the hypothesis and the conclusion
converse
switch the hypothesis and conclusion
Contrapositive
switch and negate the hypothesis and conclusion
biconditional statement
A statement that contains the phrase "if and only if"
how can you determine if a biconditional is true?
re-write the biconditional as 2 statements.2. determine whether the biconditional is true3. if not, provide a counterexample
What is a good definition?
uses clearly understood terms, is precise, and is reversible
deductive reasoning
reasoning using logic, facts, and definitions to draw a conclusion
Law of Detachment
p-->q2. p is trueconclusion: q is true
law of sylllogism
p-->q2. q--> rconclusion: p-->r
Addition Property of Equality
If a=b, then a+c=b+c
Subtraction Property of Equality
If a=b, then a-c=b-c
multiplication property of equality
If a=b, then ac=bc
Division Property of Equality
if a = b and c is not equal to 0, then a/c = b/c
Reflexive Property
a=a
Symmetric Property of Equality
if a=b, then b=a
Transitive Property of Equality
If a=b and b=c, then a=c
Substitution Property of Equality
If a=b, then a can be substituted for b in any equation or expression
proof
a convincing argument that uses deductive reasoning. logically shows why a conjecture is true
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
Congruent Complements Theorem
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
parallel lines
coplanar lines that do not intersect
parallel planes
planes that do not intersect
Transversal
a line that intersects two or more lines
alternate interior angles
angles between 2 lines and on opposite sides of a transversal
alternate exterior angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
same side interior angles
two interior angles on the same side of the transversal
same side exterior angles
two exterior angles on the same side of the transversal
corresponding angles
lie on the same side of the transversal and in corresponding positions
same side interior angle postulate
if two lines are parallel, then same side interior angles are supplementary
Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.
exterior angle
An angle formed by one side of a polygon and the extension of an adjacent side
remote interior angles
the two nonadjacent interior angles of a triangle
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
slope
the ratio of the vertical change to the horizontal change between any two points
how do you find slope?
y2-y1/x2-x1
what type of slope is this?
slope is positive
what type of slope is this?
slope is negative
what type of slope is this?
zero
what type of slope is this?
undefined
slope-intercept form
y=mx+b
point slope form
y-y1=m(x-x1)
horizontal lines
have a slope of 0
vertical line
have a undefined slope
Third Angles Theorem
if two angles of one triangle are congruent to two angles of another triangle, then the third angle are congruent
Included Angles and Sides
in the same triangle and between both angles or sides
non included angles or sides
in the same triangle but is not between both angles or sides
SSS
side side side; 3 sides of one triangle are congruent to 3 sides of another triangle
AAA
angle angle angle; 3 angles of one triangle are congruent to 3 angles of another triangle
SAS
side angle side; two sides and an included angle are congruent to that of another triangle
ASA
angle side angle; two angles and an included side are congruent to that of another triangle
AAS
angle angle side; two angles and a non-included side are congruent to that of another triangle
SSA
side side angle; two sides and a non-included angle are congruent to that of another triangle
5 theorems used to prove triangle congurence
sss, sas, asa, aas, hl
2 theorems not used to prove triangle congruence
aaa, ssa
legs
the two congruent sides of an isosceles triangle
base
the unequal side of an isosceles triangle
vertex angle
the angle formed by the legs of an isosceles triangle
base angles
the two congruent angles (opposite the legs)
Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
equilateral triangle
all of the sides and angles are congruent (also equiangular)
Note 
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