location represented by a dot, named by a capitol, print letter. ex: ˚A
straight, infinite <--------->
a flat surface that goes on infinitely in all directions.
you can picture a line that could contain points <---•A---•B---•C--->
you could picture a plane that'd contain all given points.
point where two lines meet
equal in distance; distance from point to both objects is equal.
the set of all points
two points on a line and all points between them.
one end point, goes on infinitely in one direction
made up of two rays, joined at a common end point
must have a common vertex, common side, and no common interior points
two angles that have the same measure
segments that have equal lengths
ray that cuts an angle into two even angles
intercepts a segment at its midpoint
point connection two rays of an angle
appears to be less that 90º
greater than 90º but less than 180º
angle that's 90º
from east to west.
from north to south.
segment addition postulate
used to find distance between two points by taking absolute value of difference of their coordinates.
used to find measure of an angle.
angle addition postulate
angles must be adjacent
point that divides the segment into two congruent segments
part of a conditional statement following "if" but not including the word "if." ex: "if you're a girl, then you're hot" the ____ is "you're a girl"
part of conditional statement following "then" but not including the word "then." ex: "if Ke$ha were educated, then she should not be nearly as famous" the _____ is "she would not be nearly as famous."
statement with hypothesis and conclusion; if p, then q
p implies q
p only if q
q if p
when we switch hypothesis and conclusion
shows a conditional statement is false.
both conditional and converse are both true. (all geometry definitions can be written as this).
two angles whose measures have the sum of 90º
two angles whose sides form two pairs of opposite rays and they are congruent angles
two lines that intersect to form a right angle
if 3=x, then x=3
if a=b, and b=c, then a=c
logical thinking where we use different postulates and theorems, definitions and properties to prove something.
lines that are on the same plane and don't intersect
do not lie on the same plane and do not intersect
two or more planes that do not intersect
a line that intersects two or more times in different points
angles that are between two lines
angles that are outside two lines
alternate interior angles
on opposite sides of transversal, formed with each of two lines
same-side interior angles
pair of angles between two lines and inside transversal
same relative position
at least two sides are congruent
all sides are congruent
no sides are congruent
all angles of ∆ are congruent
a line that we add to a diagram to help us prove something.
two interior angles that are not nest to an exterior angle
made up of line segments, joined only at endpoints.
does not intersect the interior
both equilateral and equiangular
segment joining two non-consecutive verticals of a polygon
angle between congruent sides
if 3 sides of one triangle are congruent to 3 sides of another triangle, triangles are congruent.
if 2 sides and included angle of one ∆ are congruent to 2 sides and the included angle of another ∆, triangles are congruent.
if 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another ∆, triangles are congruent.
if 2 angles and a non-inclined side of 1 ∆ are congruent to 2 angles and non-inclined side of another ∆, triangles are congruent.
in 2 right triangles, the hypotenuse and leg are congruent to the hypotenuse and leg of the other triangle, triangles are congruent.
segment that joins a vertex to a midpoint of opposite side of a triangle.
isosceles triangle theorem
if 2 sides of a ∆ are congruent, then the angles opposite those sides are also congruent.
perpendicular segment from a vertex to line on opposite side of a ∆
line that's perpendicular to a segment at its midpoint.
a four-sided polygon.
quadrilateral with both pairs of opp. sides parallel
segment joining two non-consecutive vertices of a polygon.
quadrilateral with four right angles
quadrilateral with four congruent sides
quadrilateral with four right angles and four congruent sides
quadrilateral with exactly one pair of parallel sides.
base of a trapezoid
parallel sides of a trapezoid are its base.
leg of trapezoid
nonparallel sides of a trapezoid are its legs.
legs are congruent and bases are congruent.
exterior angle inequality theorem
measure of an exterior angle of a ∆ is greater than the measure of either remote interior angle.
a circle diagram that may be used to represent a conditional.
the ______ of the statement "if p, then q" is "if q then p"
if not p, then not p
if not q, then not p
statement and contrapositive are logically equivalent. converse and inverse are logically equivalent.
a proof in which you 1) assume temporarily the opposite of what you're trying to prove. 2) Reason logically until you reach a contradiction of a known fact. 3) point out that the temp. assumption is false and that the conclusion is true.
statement that asks to temporarily assume that the opposite of what you're trying to prove is true.
if 2 sides of one ∆ are congruent to 2 sides of another ∆, but the included angle of the first ∆ is larger than the included angle of the second, the third side of the fist ∆ is longer than the third side of the second ∆
if 2 sides of a ∆ are congruent to 2 sides of another ∆, but the third side of the first ∆ is longer than the third side of the second ∆, then the included angle of the first ∆ is larger that the included angle of the second ∆.
names the plane
single letter on the corner of a plane that does not represent a point does this:
numbers on a number line
if lines are parallel, the _____ angles are congruent
____ points determine a line.
_____ points determine a plane.
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