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all vocab and random stuff here and there from chapters 1-6.

inductive reasoning

process of looking for patterns and making conjectures
-based on observations

counter example

an example that shows a conjecture to be false


has no dimension, but is usually represented by a small dot


extends in 1 dimension
-usually represented by a straight line with arrows at each end
-has length
-never ends (infinite)


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


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


2 rays that have the same initial point

2 rays

sides of an angle


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


less than 90 degrees


exactly 90 degrees


between 90 and 180 degrees


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)


cut in half

segment bisector

segment, ray, or line that intersects a segment at its midpoint


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


two angles who measures add to exactly 90 degrees
-can be adjacent or non adjacent


two angles whose measures add to exactly 180 degrees
-can be adjacent or non adjacent
-all linear pairs are supplementary


an unproven statement based on observations


part of a line that consist of 2 points

initial point

starting point

conditional statement

type of "logical" statement with 2 parts


setup; comes after "if"


result; comes after "then"


formed by switching the hypothesis and conclusion of a conditional statement


writing the negative of a statement (not)


formed by negating the hypothesis and conclusion of the original conditional statement


formed by negating the hypothesis and conclusion of the converse


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


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)


-change in y/change in x
-m = y2 - y1 / x2 - x1

perpendicular slopes

have slopes that are negative reciprocals of each other


line that intersects 2 or more parallel lines


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


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


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


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


point of concurrency of the perpendicular bisectors of a triangle

angle bisectors

bised the angles of a triangle
-every triangle has 3
-are concurrent


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


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


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


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


3 sides


4 sides


5 sides


6 sides


7 sides


8 sides


9 sides


10 sides


12 sides


no line containing a polygon side contains interior points


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


a quadrilateral with both pairs of opposite sides parallel


all 4 sides are congruent
-equilateral parallelogram


all 4 angles are right angles
-equiangular parallelogram


all 4 angles and all 4 sides are congruent
-equilateral and equiangular parallelogram (REGULAR)


quadrilateral that has exactly one pair of opposite sides parallel


quadrilateral with 2 pairs of consecutive, congruent sides, but opposite sides are NOT parallel

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