Home
Subjects
Create
Search
Log in
Sign up
Upgrade to remove ads
Only $2.99/month
Home
Math
Geometry
Geometry Regents
STUDY
Flashcards
Learn
Write
Spell
Test
PLAY
Match
Gravity
Terms in this set (63)
line axiom
two points determine a line:
given any two distinct points, exactly one line contains them both
each line contains at least two points
given a line there exists one point not on the ine
the distance assignment postulate
to every pair of distinct points there corresponds a unique positive number. the number is called the distance between the two points
the distance between the two point is zero if and only if the two points are not distinct
the segment existance postulate
given ray XY and line segment AB there exists exactly one point P on ray XY such that line segment XP is congruent to line segment AB
line segment extension postulate
given any two distinct points A and B, there exists a point C such that A, B, and C are collinear and C is not between A and B
angle measure assignment postulate
to every angle there corresponds a unique real number between 0 and 180. this number is called its measure
angle existence postulate
given ray XY, a point P on one side of line XY, and a real nuber k between 0 and 180, there exists exactly one ray, ray XP, such that m<PXY = k
the partition postulate
a whole is equal to the sum of its parts.
if point B is between points A and C, then line segment AB + line segment BC = line segment AC and AB + BC = AC. same with angles
existence postulates
each line segment has a unique midpoint. each angle has a unique angle bisector
trichotomy postulate
exactly one of the following is tru ( for real numbers a and b):
a<b, a>b, a=b
a whole is greater than any of its parts
if point X is a point such that A-X-B then AB>AX and AB>XB. same with angles
linear pair postulate
if 2 angles form a linear pair then they are supplementary
euclidian parallel postulate
through a given point not on a given line there exists exactly one line parallel to the given line
to prove triangles congruent
SAS (postulate), SSS, ASA, H.L (theorems)
to prove triangles similar
AA, SAS, SSS (theorems)
theorem 1
two distinct line have at most one point in common
theorem 2
If two angles are right angles, then they are congruent.
theorem 3
if two angles are complementary to the same angle then they are congruent
theorem 4
If two angles are supplementary to the same angle, then they are congruent
theorem 5
if two angles are complementary to congruent angles then they are congruent
theorem 6
if two angles are supplementary to congruent angles then they are congruent
uniqueness of a perpendicular line
through a given point on a given line there exists exactly one perpendicular to the line. through a given point not on a given line there exists exactly one perpendicular to the line
theorem 8
if two lines intersect to form congruent adjacent angles, then the lines are perpendicular
equidistance theorem 1
if two points are each equidistant from the endpoint of a line segment, then the line joining them will be the perpendicular bisector of the line segment
equidistance theorem 2
if a point lies on the perpendicular of a line segment, then it is equidistant from the endpoints of the line segment
equidistance theorem 3
if a point is equidistant from the endpoints of a line segment, then it lies on the perpendicular of the line segment
side-angle theorem
if two sides of a triangle are congruent, then the angles opposite the sides are congruent
converse of the side-angle theorem
if two angles of a triangle are congruent, then the sides opposite these angles are congruent
exterior angle inequality
the measure of an exterior angle of a triangle are congruent, then the measure of either non-adjacent interior angle
exterior angle theorem
the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
scalene inequality
if the measure of two sides of a triangle are unequal, the measures of the angles opposite these sides are unequal in the same order
the converse of the scalene inequality
if the measures of two angles of a triangle are unequal, the measures of the sides opposite these angles are unequal in the same order
triangle inequality theorem
the sum of the measures of any two sides of a triangle is greater than the measure of the third side
alternate interior angle theorem
if two lines are cut by a transversal and form a pair of congruent alternate interior angles, then the two lines are parallel
theorem 20
if two lines are cut by a transversal and form a pair of congruent corresponding angles (or a pair of congruent alternate exterior angles) then the lines are parallel
theorem 21
if two lines are cut by a transversal and form a pair of same-side interior angles that are congruent then the lines are parallel
theorem 22
if two lines are perpendicular to the same line then they are parallel to each other
converse of alternate interior angle theorem
if two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent
theorem 24
if two parallel lines are cut by a transversal , then each pair of corresponding angles (or alternate exterior angles) are congruent
theorem 25
if two parallel lines are cut by transversal, then they form same-side interior angles that are supplementary
theorem 26
if two lines are parallel, a line perpendicular to one of them is also perpendicular to the other
theorem 27
if two lines are parallel, a line parallel to one of them is also parallel to the other
theorem 28
if two lines are parallel, a line that intersects one of them also intersects the other
theorem 29
if a line segment joins the midpoints of (or bisects) two sides of a triangle, then the segment is parallel to the third side, and its the length is 1/2 the length of the third side
theorem 30
the median of a trapezoid is parallel to the base and its length is 1/2 of the sum the lengths of the bases
theorem 31
if 3 or more parallel lines intercept two or more transversals then they divide the lines proportionally
triangle proportionality theorem
if a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides proportionally
converse of triangle proportionality theorem
if a line intersects two sides of a triangle proportionally, then the line is parallel to the third side
altitude-on-hypotenuse theorem
if an altitude is drawn to the hypotenuse of a right triangle, then the altitude is the mean proportional between the segments into which it divides the hypotenuse. if an altitude is drawn to the hypotenuse of a right triangle, then each leg of the right triangle is the mean proportional between the leg and the adjacent segment on the hypotenuse
median concurrency theorem
the medians of a triangle are concurrent at a point that is 2/3 of the distance from any vertex of the triangle to the midpoint of the opposite side
additional reminders
addition and subtraction theorems for congruence. halves of congruent line segments (or angles) are congruent. doubles of congruent line segments (or angles) are congruent. reflexive property, symmetric property, and transitive property
midpoint
the point of the line segment that forms two congruent segments
line segment bisector
a line, line segment, or ray, that intersects the line segment at its midpoint
angle bisector
a ray whose endpoint is the vertex if the angle and that forms two congruent angles
linear pair
two congruent angles such that their non-common rays are mutually opposite. if the rays forming one angle are the opposite rays of the other
pythagorean theorem
of a triangle is a right triangle then the sum of the squares of the lengths of 2 sides of a triangle is = to the square of the third side
indirect proof
law of excluded middle, law of elimination
Triangle Angle Sum Theorem
the sum of the measures of the interior angles of a triangle is 180 degrees
perpendicular line distance theorem
the shortest distance from a point to a line is = to a perpendicular segment from the point to a line
angle congruency theorem
if two angles are congruent to congruent angles then they are congruent
no choice theorem
if two angles of a triangle are congruent to the 2 angles of a second triangle then the third angles are congruent
line segment bisecting the vertex angle of an isosceles triangle
if a line segment bisects the vertex angle of an isosceles triangle then it is also the median to the base
means-extremes ratio theorem
in a proportion the product of the means= product of the extremes
radii theorem
all radii of a given circle or congruent circles are congruent
THIS SET IS OFTEN IN FOLDERS WITH...
circles (Geometry regents)
54 terms
Geometry regents (area and solid geometry)
34 terms
coordinate geometry
42 terms
trigonometry
12 terms
YOU MIGHT ALSO LIKE...
GEOMETRY EXAM THEOREMS
60 terms
Honors Geometry Final - Know to Match
77 terms
Geometry terms (S1)
94 terms
Geometry Theorems
1,993 terms
OTHER SETS BY THIS CREATOR
clubs and volunteering
13 terms
family relations
9 terms
feelings and additional
15 terms
car function
11 terms