Math

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141 Terms

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collinear
points that lie on the same line
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Coplanar
points that lie on the same plane
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perpendicular lines
Lines that intersect to form right angles
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skew lines
non parallel, non coplanar (they do not intersect but go in different directions)
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midpoint
A point that divides a segment into two congruent segments
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segment bisector
either a point, line, ray or other segment that intersects a segment at its midpoint
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Midpoint formula on a coordinate plane
(x₁+x₂)/2, (y₁+y₂)/2
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midpoint formula on a number line
(a + b)/2
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angle
formed by two rays with the same endpoint
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rays
a part of a line that has a fixed starting point but no endpoint
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vertex
the point shared by both rays
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What unit is used to measure angles?
degrees
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congruent angles
angles with the same measure
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angle bisector
a ray, line, or segment, that splits an angle into two congruent angles
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acute angle
less than 90 degrees
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rigth angle
90 degrees
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obtuse angle
An angle between 90 and 180 degrees
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straight angle
an angle that measures 180 degrees
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adjacent angles
two coplanar angles with a common side, a common vertex, and no common interior points (no overlap)
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vertical angles
two angles whose sides are opposite rays (vertical angles are congruent)
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complementary angles
Two angles whose sum is 90 degrees
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supplementary angles
Two angles whose sum is 180 degrees
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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
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the distance formula
d \= √[( x₂ - x₁)² + (y₂ - y₁)²]
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perpendicular bisector of a segment
a line segment, or ray that is perpendicular to a segment at it's midpoint
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perimeter of a square
4s
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area of a square

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perimeter of a triangle
a+b+c
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Area of a triangle
1/2bh
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Perimeter of a rectangle
2(b+h)
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Area of a rectangle
bh
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circmference of a circle
2πr
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area of a circle
πr²
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inductive reasoning
reasoning based on patterns you observe
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conjecture
a conclusion you reach using inductive reasoning
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Counter example
a specific example that shows a conjecture is incorrect
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conditional
an if-then statement
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What is the "if" part of a conditional statement called?
hypothesis
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What is the "then" part of a conditional statement called?
conclusion
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negation
the negative or opposite of that statment
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Inverse
negate the hypothesis and the conclusion
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converse
switch the hypothesis and conclusion
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Contrapositive
switch and negate the hypothesis and conclusion
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biconditional statement
A statement that contains the phrase "if and only if"
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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
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What is a good definition?
uses clearly understood terms, is precise, and is reversible
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deductive reasoning
reasoning using logic, facts, and definitions to draw a conclusion
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Law of Detachment
p--\>q2. p is trueconclusion: q is true
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law of sylllogism
p--\>q2. q--\> rconclusion: p--\>r
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Addition Property of Equality
If a\=b, then a+c\=b+c
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Subtraction Property of Equality
If a\=b, then a-c\=b-c
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multiplication property of equality
If a\=b, then ac\=bc
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Division Property of Equality
if a \= b and c is not equal to 0, then a/c \= b/c
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Reflexive Property
a\=a
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Symmetric Property of Equality
if a\=b, then b\=a
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Transitive Property of Equality
If a\=b and b\=c, then a\=c
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Substitution Property of Equality
If a\=b, then a can be substituted for b in any equation or expression
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proof
a convincing argument that uses deductive reasoning. logically shows why a conjecture is true
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Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
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Congruent Complements Theorem
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
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parallel lines
coplanar lines that do not intersect
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parallel planes
planes that do not intersect
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Transversal
a line that intersects two or more lines
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alternate interior angles
angles between 2 lines and on opposite sides of a transversal
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alternate exterior angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
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same side interior angles
two interior angles on the same side of the transversal
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same side exterior angles
two exterior angles on the same side of the transversal
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corresponding angles
lie on the same side of the transversal and in corresponding positions
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same side interior angle postulate
if two lines are parallel, then same side interior angles are supplementary
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Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.
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exterior angle
An angle formed by one side of a polygon and the extension of an adjacent side
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remote interior angles
the two nonadjacent interior angles of a triangle
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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.
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slope
the ratio of the vertical change to the horizontal change between any two points
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how do you find slope?
y2-y1/x2-x1
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what type of slope is this?
slope is positive
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what type of slope is this?
slope is negative
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what type of slope is this?
zero
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what type of slope is this?
undefined
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slope-intercept form
y\=mx+b
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point slope form
y-y1\=m(x-x1)
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horizontal lines
have a slope of 0
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vertical line
have a undefined slope
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Third Angles Theorem
if two angles of one triangle are congruent to two angles of another triangle, then the third angle are congruent
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Included Angles and Sides
in the same triangle and between both angles or sides
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non included angles or sides
in the same triangle but is not between both angles or sides
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SSS
side side side; 3 sides of one triangle are congruent to 3 sides of another triangle
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AAA
angle angle angle; 3 angles of one triangle are congruent to 3 angles of another triangle
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SAS
side angle side; two sides and an included angle are congruent to that of another triangle
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ASA
angle side angle; two angles and an included side are congruent to that of another triangle
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AAS
angle angle side; two angles and a non-included side are congruent to that of another triangle
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SSA
side side angle; two sides and a non-included angle are congruent to that of another triangle
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5 theorems used to prove triangle congurence
sss, sas, asa, aas, hl
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2 theorems not used to prove triangle congruence
aaa, ssa
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legs
the two congruent sides of an isosceles triangle
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base
the unequal side of an isosceles triangle
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vertex angle
the angle formed by the legs of an isosceles triangle
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base angles
the two congruent angles (opposite the legs)
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Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
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equilateral triangle
all of the sides and angles are congruent (also equiangular)