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115 terms

Geometry Midterm Vocab -McDowell

all vocab and random stuff here and there from chapters 1-6.
STUDY
PLAY
inductive reasoning
process of looking for patterns and making conjectures
-based on observations
counter example
an example that shows a conjecture to be false
-specific
point
has no dimension, but is usually represented by a small dot
line
extends in 1 dimension
-usually represented by a straight line with arrows at each end
-has length
-never ends (infinite)
plane
extends in 2 dimensions (has length and width), usually represented by a shape that looks like a wall or a table top
-also infinite
collinear points
2 or more points that lie on the same line
coplanar points
lie on the same plane
line segment
has end points
-like a finite portion of an infinite line
ray
has an initial point then in continues infinity
opposite rays
have the same initial point, but go in opposite directions
-when looked at together, make line
points of intersection
2 or more geometric figures intersect if they have 1 or more points in common
postulate (axiom)
rule that is accepted without proof
distance formula
d = square root of (x2-x1) squared + (y2-y1) squared
angle
2 rays that have the same initial point
2 rays
sides of an angle
vertex
shared initial point
congruent angles
angles that have the same measure
interior of an angle
between the points on each side of the angle
exterior of an angle
points NOT on the sides or in the interior of an angle
acute
less than 90 degrees
right
exactly 90 degrees
obtuse
between 90 and 180 degrees
straight
exactly 180 degrees
adjacent angles
common side and vertex, but no other interior points in common
midpoint of a segment
point in the exact middle of a segment (cuts it in half)
bisect
cut in half
segment bisector
segment, ray, or line that intersects a segment at its midpoint
construction
geometric drawing that uses a limited set of tools (compass and straight edge)
midpoint formula
for end points
-m = (x1 + x2 /2, y1 + y2/2)
angle bisector
ray that divides an angle into 2 adjacent angles that are congruent
vertical angles
two angles whose sides form 2 pairs of opposite rays (2 intersecting lines)
-shared vertex in middle
linear pair
two adjacent angles whose non common sides are opposite rays
complementary
two angles who measures add to exactly 90 degrees
-can be adjacent or non adjacent
supplementary
two angles whose measures add to exactly 180 degrees
-can be adjacent or non adjacent
-all linear pairs are supplementary
conjecture
an unproven statement based on observations
endpoints
part of a line that consist of 2 points
initial point
starting point
conditional statement
type of "logical" statement with 2 parts
hypothesis
setup; comes after "if"
conclusion
result; comes after "then"
converse
formed by switching the hypothesis and conclusion of a conditional statement
negation
writing the negative of a statement (not)
inverse
formed by negating the hypothesis and conclusion of the original conditional statement
contrapositive
formed by negating the hypothesis and conclusion of the converse
definition
uses known words to describe a new word or concept
perpendicular lines
lines that intersect to form right angles
line perpendicular to a plane
that intersects a plane at a point so that it forms a right angle with every line in that plane
biconditional statements
contain the phrase "if and only if" (Or IFF); same as writing a conditional statement and its converse together
theorem
statement that follows as a result of other true statements
-must be proven
two column proof
has numbered statements and reasons that show the logical order of an argument
paragraph proof
proof written in paragraph form
deductive reasoning
uses facts, definitions, and accepted properties in a logical order to write a logical argument
parallel lines
coplanar, but never intersect
skew lines
not coplanar, but never intersect
parallel planes
2 or more planes that never intersect
corresponding angles
occupy same positions on each parallel line
alternate interior angles
between inside the 2 parallel lines, on opposite sides of transversal
alternate exterior angles
between outside the 2 parallel lines, on opposite sides of transversal
consecutive interior angles
between 2 parallel lines on same side of the transversal
flow proof
uses arrows to show the flow of logical argument (reasons are usually written below the statements)
slope
-rise/run
-change in y/change in x
-m = y2 - y1 / x2 - x1
perpendicular slopes
have slopes that are negative reciprocals of each other
transversal
line that intersects 2 or more parallel lines
equilateral
all 3 sides are the same length
isosceles triangle
triangle where at least 2 sides are congruent
scalene triangle
triangle where all sides are different length
acute triangle
all 3 angles are acute
equiangular triangle
all 3 angles have the same measure
obtuse triangle
1 angle is obtuse
right triangle
1 angle is 90 degrees
hypotenuse
the side opposite the right angle
adjacent sides
2 sides of the triangle sharing a common vertex
opposite side
the 3rd side of a triangle with adjacent sides
legs
the 2 sides of a right triangle that make the right angle
-perpendicular to each other
congruent figures
exactly same size and shape
corresponding angles
angles in the same position
corresponding sides
sides in the same position
base angles
2 angles in an isosceles triangle that are adjacent to the base
-non congruent side
vertex angle
in an isosceles triangle: angle opposite to the base; sides are the 2 congruent legs of the triangle
coordinate proof
involves placing a geometric figure in the coordinate plane
-then we use distance and midpoint formulas long with postulates, theorems, etc, to prove statements
perpendicular bisector
segment, line, or ray, that is perpendicular to a segment at its midpoint
equidistant
the same distance from something
distance from a point to a line
the length of the perpendicular segment from the point to the line
perpendicular bisector of a triangle
a line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side
-every triangle has 3
-all intersect at one point
concurrent lines
3 or more lines that intersect at the same point
point of concurrency
point where lines intersect at same point
circumcenter
point of concurrency of the perpendicular bisectors of a triangle
angle bisectors
bised the angles of a triangle
-every triangle has 3
-are concurrent
incenter
point of concurrency of angle bisectors
-always inside the triangle
-equidistant from all 3 sides of the triangle
median of a triangle
a segment whose endpoints are vertex of a triangle and the midpoint of the opposite side
-every triangle has 3
-are concurrent
centroid
point of concurrency of medians of a triangle
-always inside the triangle
-balance point for the triangle
altitude of a triangle
perpendicular segment from a vertex to the opposite side (or the line containing the opposite side)
-every triangle has 3
-are concurrent
orthocenter
point of concurrency of altitude of a triangle
-acute triangle: inside
-right triangle: on the triangle, vertex of the right angle
-obtuse triangle: outside
midsegment of a triangle
segment that connects the midpoints of 2 sides of a triangle
indirect proof
prove a statement is true by first assuming that its opposite is true
-if assumption leads to an impossibility, then the original must be truel
polygon
a plane figure formed by 3 or more segments so that each segment intersects exactly 2 others at each end point
-no curves, gaps, overlaps, or criss crosses
triangle
3 sides
quadrilateral
4 sides
pentagon
5 sides
hexagon
6 sides
heptagon
7 sides
octagon
8 sides
nonagon
9 sides
decagon
10 sides
dodecagon
12 sides
convex
no line containing a polygon side contains interior points
concave
the extended line of at least 1 side contains points in the interior of the polygon
regular polygon
polygon that is equilateral and equiangular
diagonal of a polygon
segment that joins 2 nonconsecutive vertices
parallelogram
a quadrilateral with both pairs of opposite sides parallel
rhombus
all 4 sides are congruent
-equilateral parallelogram
rectangle
all 4 angles are right angles
-equiangular parallelogram
square
all 4 angles and all 4 sides are congruent
-equilateral and equiangular parallelogram (REGULAR)
trapezoid
quadrilateral that has exactly one pair of opposite sides parallel
kite
quadrilateral with 2 pairs of consecutive, congruent sides, but opposite sides are NOT parallel