point
location
line
infinite straight line of points going on forever in both directions
plane
flat space made of points
ray
goes on in one direction
bisect
divide in two equal parts
midpoint
middle of a segment
collinear
points on the same line
coplanar
points on the same plane but are not all on the same line
opposite rays
two rays that share an endpoint and extend outward at 180 degrees and forms a line
space
where points are
angle
A figure formed by two rays with a common endpoint
bisector
A ray that divides an angle into two congruent angles
congruent
the same, equal
vertex
Each angular point of a polygon, polyhedron, or other figure.
Complementary Angles
add up to 90 degrees
Supplementary Angles
add up to 180 degrees
vertical angles
A pair of opposite congruent angles formed by intersecting lines
The X
adjacent angles
two angles next to each other which add up to 180 degreed
linear pair
adjacent, add up to 180 degrees
acute angles
angles less than 90 degrees
right angles
angles that are exactly 90 degrees and usually have a box where the perpendicular lines meet
obtuse angles
angles greater than 90 degrees but less than 180 degrees
straight angles
angles that are exactly 180 degrees
polygon
a 2-Dimensional closed figire
concave
when you are able to draw a straight diagonal line between two points on the outside of the figure, it is concave
convex
puffed out
regular polygon
all sides and angles are equal
equilateral and equiangular
perpendicular
when two or more lines intersect at a right angle
inductive reasoning
generalizations based on a large number of specific observations
conditional
an IF, THEN statement
hypothesis
the statement after "if" in a conditional
conclusion
the statement after "then" in a conditional
conjecture
inference based on guesses
counter example
proves a conditional false
converse
switching the hypothesis and conclusion in a conditional
inverse
taking the opposite of a conjecture (no, not)
contrapositive
taking the inverse and converse
reflexive property
same on both sides
a=a
symmetric property
swapping things on either side of the =
if a=b, then b=a
transitive property
if a=b, and b=c, then a=c
associative property
move parenthesis on that side of the =
(a+b)+c=x a+(b+c)=x
commutative property
addition and multiplication order doesn't matter
a+b+c c+a+b x
y
x y
x
z
distributive property (distribution)
multiply things on the inside of ( ) by the thing on the outside
a(b+c) ab+ac
substitution property (substitution)
replace something with something else of equal value
if a=b, and b+c=d, then a+c=d
segment addition postulate
If b is between a and c, then ab + bc =ac
angle addition postulate
angles can be added together if they are adjacent.
If d is in the interior of angle abc, then abd+bdc=abc
transversal
a line that intersects two or more lines
corresponding angles
angles in the same place on different lines
alternate interior angles
angles between the two lines and on opposite sides of the transversal
alternate exterior angles
angles outside the two lines and on opposite sides of the transversal
consecutive interior angles
angles between the two lines and on same sides of the transversal
skew lines
lines that do not touch and are on different planes and are not parallel
parallel
two lines that do not touch and go on forever in the same direction
triangle
a figure that has three sides and has three angles that add up to 180.
obtuse triangle
a triangle with an angle that measures more than 90 but less than 180
acute triangle
a triangle with an angle that measures more than 0 but less than 90
right triange
a triangle with an angle that measures exactly 90
equiangular triangle
a triangle with all congruent angles
scalene triangle
a triangle with no congruent sides and angles
isosceles triangle
a triangle with two congruent sides and angles
exterior angle
an angle on the outside of something (triangle)
remote interior angles
the two angles of a triangle nonadjacent to the exterior angle
triangle sum theorem
the sum of the measures of the angles of a triangle is 180
triangle exterior angle
the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
theorem
can be proven
third angle theorem
if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent
congruent triangles
a pair of triangles whose sides and angles are the same
median
a segment that goes from the midpoint of another segment to the vertex of the triangle
altitude
a segment that is perpendicular to the base and goes to the vertex of the triangle
perpendicular bisector
a segment that goes from the midpoint of the base and goes to the vertex of the triangle
angle bisector
a segment that divides the vertex of the triangle into two equal parts
triangle inequalitites
if the two smallest sides add up to be greater than the third side
perpendicular bisector theorem
a line that is perpendicular to a segment at its midpoint
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
proportion
a statement that two ratios are equal
similar figures
figures that have the same shape but not necessarily the same size
similarity ratio
the ratio of the lengths of corresponding sides
similarity statement
a statement saying that two figures are similar
AA~
if 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the triangles are similar
SAS~
if the ratios of the measures of two pairs of corresponding sides of two triagnles are equal and their included angles are congruent, the the triangles are similar
SSS~
if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar
midsegment
segment that connects the midpoints of two sides of a triangle
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
side splitter theorem
if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally
side splitter corollary
if a line parallel to one side of a triangle intersects the other two sides in different points, it cuts off segments proportional to the sides
perimeter ratio
the ratio of the perimeter of two similar figures; is equal to the length/similarity ratio
area ratio
square (x^2) of the side ratio
rationalize
to eliminate the radicals from the denominator of a fraction
Pythagorean Theorem
use of a2+b2=c2 to find the missing side of a right triangle
Converse of Pythagorean Theorem
if c2=a2+b2, then the triangle is a right triangle
Geometric Mean
x...b
--=--
a...x
Special Right Triangles
a 30, 60, 90 triangle or a 45, 45, 90 triangle
Sine
opposite side over hypotenuse
Cosine
adjacent side over hypotenuse
Tangent
opposite side over adjacent side
Reference Angle
positive acute angle formed by the x-axis and the terminal side of the given angle
Converse of Pythagorean Theorem
if c2=a2+b2, then the triangles is right
Angle of Elevation
the angle formed by a horizontal line and the line of sight to an object above the horizontal line
Angle of Depression
the angle formed by a horizontal line and the line of sight to an object below the horizontal line
Quadrilateral
4 sided polygon
Exterior Angle Sum
sum always equals 360
Interior Angle Sum
(n-2)180
Diagonal
a straight line connecting any two vertices of a polygon that are not adjacent
Square
a quadrilateral with 4 sides that are equal and has all 90 degree angles
Rhombus
a parallelogram with four equal sides
Rectangle
a quadrilateral in which the opposite sides are parallel, all angles are 90 degrees
Parallelogram
a quadrilateral whose opposite sides are both parallel and equal in length
Kite
a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent
Trapezoid
a quadrilateral with exactly one pair of parallel sides
Isosceles Trapezoid
a trapezoid with congruent legs
Interior Angle
angles inside parallel lines cut by a transversal
Exterior Angle
an angle formed by one side of a triangle and the extension of another side
Median of Trapezoid
�(b?+b?)
point
location
line
infinite straight line of points going on forever in both directions
plane
flat space made of points
ray
goes on in one direction
bisect
divide in two equal parts
midpoint
middle of a segment
collinear
points on the same line
coplanar
points on the same plane but are not all on the same line
opposite rays
two rays that share an endpoint and extend outward at 180 degrees and forms a line
space
where points are
angle
A figure formed by two rays with a common endpoint
bisector
A ray that divides an angle into two congruent angles
congruent
the same, equal
vertex
Each angular point of a polygon, polyhedron, or other figure.
Complementary Angles
add up to 90 degrees
Supplementary Angles
add up to 180 degrees
vertical angles
A pair of opposite congruent angles formed by intersecting lines
The X
adjacent angles
two angles next to each other which add up to 180 degreed
linear pair
adjacent, add up to 180 degrees
acute angles
angles less than 90 degrees
right angles
angles that are exactly 90 degrees and usually have a box where the perpendicular lines meet
obtuse angles
angles greater than 90 degrees but less than 180 degrees
straight angles
angles that are exactly 180 degrees
polygon
a 2-Dimensional closed figire
concave
when you are able to draw a straight diagonal line between two points on the outside of the figure, it is concave
convex
puffed out
regular polygon
all sides and angles are equal
equilateral and equiangular
perpendicular
when two or more lines intersect at a right angle
inductive reasoning
generalizations based on a large number of specific observations
conditional
an IF, THEN statement
hypothesis
the statement after "if" in a conditional
conclusion
the statement after "then" in a conditional
conjecture
inference based on guesses
counter example
proves a conditional false
converse
switching the hypothesis and conclusion in a conditional
inverse
taking the opposite of a conjecture (no, not)
contrapositive
taking the inverse and converse
reflexive property
same on both sides
a=a
symmetric property
swapping things on either side of the =
if a=b, then b=a
transitive property
if a=b, and b=c, then a=c
associative property
move parenthesis on that side of the =
(a+b)+c=x a+(b+c)=x
commutative property
addition and multiplication order doesn't matter
a+b+c c+a+b x
y
x y
x
z
distributive property (distribution)
multiply things on the inside of ( ) by the thing on the outside
a(b+c) ab+ac
substitution property (substitution)
replace something with something else of equal value
if a=b, and b+c=d, then a+c=d
segment addition postulate
If b is between a and c, then ab + bc =ac
angle addition postulate
angles can be added together if they are adjacent.
If d is in the interior of angle abc, then abd+bdc=abc
transversal
a line that intersects two or more lines
corresponding angles
angles in the same place on different lines
alternate interior angles
angles between the two lines and on opposite sides of the transversal
alternate exterior angles
angles outside the two lines and on opposite sides of the transversal
consecutive interior angles
angles between the two lines and on same sides of the transversal
skew lines
lines that do not touch and are on different planes and are not parallel
parallel
two lines that do not touch and go on forever in the same direction
triangle
a figure that has three sides and has three angles that add up to 180.
obtuse triangle
a triangle with an angle that measures more than 90 but less than 180
acute triangle
a triangle with an angle that measures more than 0 but less than 90
right triange
a triangle with an angle that measures exactly 90
equiangular triangle
a triangle with all congruent angles
scalene triangle
a triangle with no congruent sides and angles
isosceles triangle
a triangle with two congruent sides and angles
exterior angle
an angle on the outside of something (triangle)
remote interior angles
the two angles of a triangle nonadjacent to the exterior angle
triangle sum theorem
the sum of the measures of the angles of a triangle is 180
triangle exterior angle
the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
theorem
can be proven
third angle theorem
if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent
congruent triangles
a pair of triangles whose sides and angles are the same
median
a segment that goes from the midpoint of another segment to the vertex of the triangle
altitude
a segment that is perpendicular to the base and goes to the vertex of the triangle
perpendicular bisector
a segment that goes from the midpoint of the base and goes to the vertex of the triangle
angle bisector
a segment that divides the vertex of the triangle into two equal parts
triangle inequalitites
if the two smallest sides add up to be greater than the third side
perpendicular bisector theorem
a line that is perpendicular to a segment at its midpoint
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
proportion
a statement that two ratios are equal
similar figures
figures that have the same shape but not necessarily the same size
similarity ratio
the ratio of the lengths of corresponding sides
similarity statement
a statement saying that two figures are similar
AA~
if 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the triangles are similar
SAS~
if the ratios of the measures of two pairs of corresponding sides of two triagnles are equal and their included angles are congruent, the the triangles are similar
SSS~
if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar
midsegment
segment that connects the midpoints of two sides of a triangle
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
side splitter theorem
if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally
side splitter corollary
if a line parallel to one side of a triangle intersects the other two sides in different points, it cuts off segments proportional to the sides
perimeter ratio
the ratio of the perimeter of two similar figures; is equal to the length/similarity ratio
area ratio
square (x^2) of the side ratio
rationalize
to eliminate the radicals from the denominator of a fraction
Pythagorean Theorem
use of a2+b2=c2 to find the missing side of a right triangle
Converse of Pythagorean Theorem
if c2=a2+b2, then the triangle is a right triangle
Geometric Mean
x...b
--=--
a...x
Special Right Triangles
a 30, 60, 90 triangle or a 45, 45, 90 triangle
Sine
opposite side over hypotenuse
Cosine
adjacent side over hypotenuse
Tangent
opposite side over adjacent side
Reference Angle
positive acute angle formed by the x-axis and the terminal side of the given angle
Converse of Pythagorean Theorem
if c2=a2+b2, then the triangles is right
Angle of Elevation
the angle formed by a horizontal line and the line of sight to an object above the horizontal line
Angle of Depression
the angle formed by a horizontal line and the line of sight to an object below the horizontal line
Quadrilateral
4 sided polygon
Exterior Angle Sum
sum always equals 360
Interior Angle Sum
(n-2)180
Diagonal
a straight line connecting any two vertices of a polygon that are not adjacent
Square
a quadrilateral with 4 sides that are equal and has all 90 degree angles
Rhombus
a parallelogram with four equal sides
Rectangle
a quadrilateral in which the opposite sides are parallel, all angles are 90 degrees
Parallelogram
a quadrilateral whose opposite sides are both parallel and equal in length
Kite
a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent
Trapezoid
a quadrilateral with exactly one pair of parallel sides
Isosceles Trapezoid
a trapezoid with congruent legs
Interior Angle
angles inside parallel lines cut by a transversal
Exterior Angle
an angle formed by one side of a triangle and the extension of another side
Median of Trapezoid
�(b?+b?)