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Geometry Midterm Exam

STUDY
PLAY
point
location represented by a dot, named by a capitol, print letter. ex: ˚A
line
straight, infinite <--------->
plane
a flat surface that goes on infinitely in all directions.
collinear
you can picture a line that could contain points <---•A---•B---•C--->
coplanar
you could picture a plane that'd contain all given points.
intersection
point where two lines meet
equidistant
equal in distance; distance from point to both objects is equal.
space
the set of all points
segment
two points on a line and all points between them.
ray
one end point, goes on infinitely in one direction
angle
made up of two rays, joined at a common end point
adjacent angles
must have a common vertex, common side, and no common interior points
congruent angles
two angles that have the same measure
congruent segments
segments that have equal lengths
angle bisector
ray that cuts an angle into two even angles
segment bisector
intercepts a segment at its midpoint
vertex
point connection two rays of an angle
acute angle
appears to be less that 90º
obtuse angle
greater than 90º but less than 180º
right angle
angle that's 90º
straight angle
180º
horizontal
from east to west.
verticle
from north to south.
segment addition postulate
--•X--•Y-------•Z-- XY+YZ=XZ
ruler postulate
used to find distance between two points by taking absolute value of difference of their coordinates.
protractor postulate
used to find measure of an angle.
angle addition postulate
angles must be adjacent
midpoint
point that divides the segment into two congruent segments
hypothesis
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"
conclusion
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."
conditional
statement with hypothesis and conclusion; if p, then q
p implies q
p only if q
q if p
converse
when we switch hypothesis and conclusion
counterexapmple
shows a conditional statement is false.
biconditional
both conditional and converse are both true. (all geometry definitions can be written as this).
complementary angles
two angles whose measures have the sum of 90º
vertical angles
two angles whose sides form two pairs of opposite rays and they are congruent angles
perpendicular lines
two lines that intersect to form a right angle
symmetric property
if 3=x, then x=3
transitive property
if a=b, and b=c, then a=c
deductive reasoning
logical thinking where we use different postulates and theorems, definitions and properties to prove something.
parallel lines
lines that are on the same plane and don't intersect
skew lines
do not lie on the same plane and do not intersect
parallel planes
two or more planes that do not intersect
transversal
a line that intersects two or more times in different points
interior angles
angles that are between two lines
exterior angles
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
corresponding angles
same relative position
isosceles triangle
at least two sides are congruent
equilateral triangle
all sides are congruent
scalene triangle
no sides are congruent
equiangular
all angles of ∆ are congruent
auxilary line
a line that we add to a diagram to help us prove something.
remote interior
two interior angles that are not nest to an exterior angle
polygon
made up of line segments, joined only at endpoints.
convex polygon
does not intersect the interior
regular polygon
both equilateral and equiangular
diagnol
segment joining two non-consecutive verticals of a polygon
congruent
same size/shape
included angle
angle between congruent sides
SSS postulate
if 3 sides of one triangle are congruent to 3 sides of another triangle, triangles are congruent.
SAS postulate
if 2 sides and included angle of one ∆ are congruent to 2 sides and the included angle of another ∆, triangles are congruent.
ASA postulate
if 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another ∆, triangles are congruent.
AAS postulate
if 2 angles and a non-inclined side of 1 ∆ are congruent to 2 angles and non-inclined side of another ∆, triangles are congruent.
HL theorem
in 2 right triangles, the hypotenuse and leg are congruent to the hypotenuse and leg of the other triangle, triangles are congruent.
median
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.
altitude
perpendicular segment from a vertex to line on opposite side of a ∆
perpendicular bisector
line that's perpendicular to a segment at its midpoint.
quadrilateral
a four-sided polygon.
parallelogram
quadrilateral with both pairs of opp. sides parallel
diagonal
segment joining two non-consecutive vertices of a polygon.
rectangle
quadrilateral with four right angles
rhombus
quadrilateral with four congruent sides
square
quadrilateral with four right angles and four congruent sides
trapezoid
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.
isosceles trapezoid
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.
venn diagram
a circle diagram that may be used to represent a conditional.
converse
the ______ of the statement "if p, then q" is "if q then p"
inverse
if not p, then not p
contrapositive
if not q, then not p
equivalent
statement and contrapositive are logically equivalent. converse and inverse are logically equivalent.
indirect proof
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.
temporary assumption
statement that asks to temporarily assume that the opposite of what you're trying to prove is true.
SAS inequality
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 ∆
SSS inequality
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:
coordinates
numbers on a number line
corresponding
if lines are parallel, the _____ angles are congruent
triangle
3 sides
quadrilateral
4 sides
pentagon
5 sides
hexagon
6 sides
heptagon
7 sides
octagon
8 sides
nonagon
9 sides
decagon
10 sides
dodecgon
12 sides
2
____ points determine a line.
3
_____ points determine a plane.