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123 Cards in this Set

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Supplement theorem
If two angles form a linear pair then they are supplementary angles
complement theorem
if the noncommon sides of two adjacent angles form a right angle then the angles are complementary angles.
congruence of angles
are reflexive, symetric, and transitive
Theorem angles suppl to the...
angles suppl to same angle or congruent angles are congruent
theorem

angles compl
angles compl to same angle or congru. angles are congru
vert angle theorem
if two angles are vert angles then they ar congru
perpendicular lines intersect to
to form 4 right angles
all right angles are
congruent
Perpendicular lines form..
congruent adj angles.
if two lines are congruent and suppl then
each angle is a rght angle
if 2 congru angles form a linear pair then
they are right angles
CA means
if 2 lines are //, cut by a transversal, then each pr of corre angles is con.
AIA
If 2 // lines cut by a trans then each pr of aia is con
CIA
If two // lines cut by transve then ea pr of consec int angl is suppl
AEA
If 2 // lines cut by transve then each pr of AEA is congruent
Perpen transversal TH
in a plane, if a line is perpen to one then perpen to other
2 nonvertical lines have the same slope
if and only if they are //
2 nonvert lines are perpen
if and only if the product of their slopes are -1
if 2 lines in a plane are cut by a trans
so that the corres angles are congru then the lines are //
// post
if there is a line and a point not on al ine then there exsist one line that is exactly one though the pnt that is // to given line
if alt ext angles are congru then..
lines are //
if cons int angles are suppl then
the lines are //
if alt angles are congru then...
the lines are //
if 2 lines are perpen to the samelines then
they are //
in a plane if 2 lines are each equidistant from the thrid
then two lines are // to ea other
Angle sum TH
The sum of a whole tiangle is 180
third angle TH
If 2 angles of one triangle are congruent to 2 angles of a second tri then the 3rd angles of the tri are congru
EXT angle TH
The measure of an ext angle of a tri is equall to the sum of the measures of the two remot int angles
the acute angles of a rght tri are
are comple
There can only be 1 blank and 1 balnk in a tri at most
right and obtuse
congruence of tri is
reflex symm, and transitive
SSS
If the side of one tri is congru to the sides of the second tri then the tri are congru
SAS
if 2 sides and the inclu side of one triangle are congru to 2 sides and the inclu of another tri the tri are con
ASA
If 2 angles and the inclu side of one tri are con to 2 and the sides and the inclu angle of another tri then tris are congru
AAS
angle angle side
LL
if the legs of a right tri are con then the tri are congru
HA
if the hypotenuse and acute of one rght tri , and the hypo is con to the acuute then the tris are congru
LA
If a leg and a acute angle are con on a rght tri then tris are congru
HL
If the Hypo and leg are con in a rght tri then tris are con
Con isos TH if 2 angles of a tri are congu
then the sides opp angles are congru
I tri is =lateral if
it it is = angular
ea of an equilangular tri measurs
60
ANy point on the perpen bisect of a seg is =distant from the
endpoint of a segment
any point on a =distant from the endpoints of a seg lies on the perpen
bisector of the seg
circum center TH
The circumcenter of a tri is equal dist from the vercies of the tri
ANy point on the bisect is equal dist from the sides of an angle lies
on the angle bisect
incenter TH
The incenter of a tri is = dist from ea side of the tri
CEntroid Th
The centroid of a tri is located 2/3 of teh dist from a vert to the midpt of te opp the vertex on a median
Ext Angle In=ity TH
If an angle is an EXT angle of a tri then its measure is greater than the measure of either of its corr remote int angles
if one angle of a tri has a greater measure than another angles
then the side opp the greate angle is longer than the side opp the lesser angle
The perpen seg from a point to a line is
shortest seg from point to the line
The perpern seg from a pnt to a place is
the shortest seg from point to the plane
tri in= th
the sum of any two sides of a tri id greater thsnthe 3rd side
acute angle
An angle of less than 90°.
acute tri
triangle whose interior angles are all acute
adj andgles
Either of two angles having a common side and a common vertex
AEA
Angles 1, 2, 3, and 4 are all exterior angles. Angles 1 and 4 are alternate exterior angles. Angles 2 and 3 are also alternate exterior angles. Line t (in red) is called a transversal, a line crossing two or more lines.
AIA
Angles 1 and 4 are alternate interior angles. Angles 2 and 3 are also alternate interior angles. Line t (in red) is called a transversal, a line crossing two or more lines. When the transversal cuts through 2 parallel lines, the alternate interior angles formed have a special relationship
altitude
The perpendicular distance between a vertex of a triangle and the side opposite that vertex. Sometimes called the height of a triangle. Also, sometimes the line segment itself is referred to as the altitude
angle
Region between two rays
angle bisector
A segment or ray that shares a common endpoint with an angle and divides the angle into two equal parts.
Biconditional
a conjunction of a conditional state and its conve
centroid
The point of intersection of the medians of a triangle.
circumcenter
point of intersection of the perpendicular bisectors of the sides of a given triangle
collinear
Points are collinear if they lie on the same straight line.
compl angles
Complementary angles are two angles whose sum is 90 degrees.
conclusion
the statement that follows the word then
concurrent lines
3 or more lines that inter sect at a common point
condition stat
a if then state
congruent
having the same measure
congruent tri
Triangles that have the same size and shape.
conjecture
an educated guess based on known info
CIA
the 2 middle top bottom #
contrapt
formed statement from the converse of a state
converese
The statement formed by hypo and conlu of the converse of a conditional state
convex poly
a polygon where no line contains both sides of the poly gon
coplaner
Set of points, lines, rays, line segments, etc., that lie in the same plane
corresponding angles
Angles that have the same relative positions in geometric figures.
counter example
to show that a state isnt always true
condition stat
a if then state
hypothesis
follows the word if the condition stat
congruent
having the same measure
if-then statement
a compound statement it goes if A then B
congruent tri
Triangles that have the same size and shape.
disjunction
a compound statement frmed by joining 2 or more statements
conjecture
an educated guess based on known info
incenter
The center of a circle inscribed in a given triangle.
CIA
the 2 middle top bottom #
contrapt
formed statement from the converse of a state
converese
The statement formed by hypo and conlu of the converse of a conditional state
convex poly
a polygon where no line contains both sides of the poly gon
coplaner
Set of points, lines, rays, line segments, etc., that lie in the same plane
corresponding angles
Angles that have the same relative positions in geometric figures.
counter example
to show that a state isnt always true
hypothesis
follows the word if the condition stat
if-then statement
a compound statement it goes if A then B
disjunction
a compound statement frmed by joining 2 or more statements
incenter
The center of a circle inscribed in a given triangle.
condition stat
a if then state
congruent
having the same measure
congruent tri
Triangles that have the same size and shape.
conjecture
an educated guess based on known info
CIA
the 2 middle top bottom #
contrapt
formed statement from the converse of a state
converese
The statement formed by hypo and conlu of the converse of a conditional state
convex poly
a polygon where no line contains both sides of the poly gon
coplaner
Set of points, lines, rays, line segments, etc., that lie in the same plane
corresponding angles
Angles that have the same relative positions in geometric figures.
counter example
to show that a state isnt always true
hypothesis
follows the word if the condition stat
if-then statement
a compound statement it goes if A then B
disjunction
a compound statement frmed by joining 2 or more statements
incenter
The center of a circle inscribed in a given triangle.
included angle
an angle formed by 2 sides
included side
the side of the tri the is part of the 2 angles
indirect proof
when you use the assume
inductive reasoning
arrived by deductive reasoning
inverse
negating both the hypothesis and conclusion
isoscelese tri
A triangle with at least two sides having equal lengths.
law of detachment
if p then q is true p is true, then so is q
line
One of the basic undefined terms of geometry. A line has no thickness but its length goes on forever in two directions., at least 2 pnts
line seg
The part of a line between two points on the line. Sometimes referred to as a segment.
linear pair
Two adjacent angles that form a straight line