highschool geometry, algebra 2, triginometry, pre-calc/calculus
A word without a formal definition.
A point has no dimension. It is represented by a dot.
A line has one dimension. It is represented by a line with two arrowheads.
A plane has two dimensions. It is represented by a shape that looks like a floor or a wall.
Points that lie on the same line.
Points that lie in the same plane.
Terms that can be described using known words.
Part of a line that consists of two points, called endpoints, and all the points on the line between the endpoints.
The ray "AB" consists of the endpoint "A" and all points on line "AB" that lie on the same side of "A" as "B."
2 rays that have the same endpoint and go in opposite directions forming a line.
A rule that is excepted withought proof.
A rule that can be proved.
The real number that corresponds to a point.
The distance between two points "A" and "B," written as "AB," is the absolute value of the difference of the coordinates of "A" and"B."
When three points are collinear, you can say that one point is between the other two.
Line segments that have the same length.
segment addition postulate
AB + BC = AC.
2 angles whose sum is 90 degrees.
two angles whose sum is 180 degrees.
two angles that share a common vertex or side, but have no common interior points.
two adjacent angles are a linear pair if their noncommon sides are opposite rays.
two angles are vertical angles if their sides form two pairs of opposite rays.
an unproven statement that is based on observations.
the process of finding a pattern for specific cases and then writing a conjecture for the general case.
a specific case for which the conjecture is false.
a logical statement that has 2 parts: a hypothesis and a conclusion.
a form of a conditional statement in which the "if" part contains the hypothesis and the "then" part contains the conclusion.
the "if" part of a conditional statement.
the "then" part of a conditional statement.
the opposite of the original statement.
the part of a conditional statement that is formed by negating both the hypothesis and conclusion.
the part thats formed by negating both the hypothesis and the conclusion.
the part that is formed by writing the converse and then negating both the hypothesis and the conclusion.
2 statements that are both true or both false.
2 lines that intersect to form a right angle.
a statement that contains the phrase "if, and only if"
using facts, definitions, excepted properties, and laws of logic to form a logical argument.
line perpendicular to a plane
if, and only if, the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.
through any two points there exists exactly one line
a line contains at least 2 points
if 2 lines intersect, then their intersection is exactly one point
~postulate #4 was executed before its people and sadly, no longer exists :(
through any 3 noncollinear points there exists exactly one plane
a plane contains at least 3 noncollinear points
if 2 points lie in a plane then the line containing them [also] lies in the plane
if two planes intersect, then their intersection is a line
postulate 11 1/2: (don't ask me how)
through any 3 noncollinear points, there exists exactly one plane
if a = b, then a+c = b+c.
if a = b, then a - c = b - c.
if a = b, then a x c = b x c.
if a = b, then a\c = b\c.
if a = b, then "a" can be subbed for "b"
A logical argument that shows a statement is true.
Has numbered statements and corresponding reasons that show an argument in logical order.
a statement that can be proven
two lines that do not intersect and are co-planar
two lines that do not intersect and are NOT coplanar
two planes that do not intersect
a line that intersects two or more coplanar lines at different points
two angles that have corresponding positions
alternate interior angles
two angles that lie between the two lines and on opposite sides of the transversal
alternate exterior angles
two angles that lie outside the two lines and on opposite sides of the transversal
consecutive interior angle
two angles that lie between the two lines and on the same side of the transversal
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
the general form of a linear equation in slope-intercept form is 'y=mx+b' where "m" is the slope and "b" is the Y-intercept
the general form of a linear equation in standard form is Ax+By=c, where "A" and "B" are not both zero
distance from a point to a line
the length of the perpendicular segment from the point to the line
a polygon with 3 sides
when the sides of a polygon are extended, the original angles are the interior angles
when the sides of a polygon are extended, the angles that form linear pairs with the interior angles are the exterior angles
corollary to a theorem
a statement that can be proved easily using a theorem
where all the parts of one figure are congruent to the corresponding parts of the other figure
in congruent polygons, the corresponding parts are the corresponding sides and the corresponding angles
leg of a right triangle
in a right triangle, a side adjacent the right angle is called a leg
in a right triangle, the side opposite the right angle is called the hypotenuse
the two congruent sides of an isosceles triangle
the angle formed by the legs in an isosceles triangle
the side of an isosceles triangle that is not a leg
the two isosceles angles congruent to the base
an operation that moves or changes a geometric figure in some way to produce a new figure
the new figure produced by a transformation
moves every point of a figure the same distance in the same direction
uses a "LINE OF REFLECTION" to create a mirror image of the original figure
turns a figure about a fixed print, called the "CENTER OF ROTATION"
midsegment of a triangle
a segment that connects the midpoints of two sides of a triangle
involves placing geometric figures in a coordinate plane
a segment, ray, line, or plane that is perpendicular to a segment at its midpoint
if a point is the same distance between each two figures
when three or more lines/rays or segments intersect in the same point
point of concurrency
the point of intersection of concurrent lines, rays, or segments.
the point of concurrency of the three bisectors of a triangle