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Vocab Terms & Theorems/Postulates
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Gravity
Terms in this set (116)
acute angle
an angle with a degree measure less than 90 degrees
acute triangle
a triangle in which all of the angles are acute angles
adjacent angles
two angles that lie in the same plane, have a common vertex, and a common side, but no common interior points
alternate exterior angles
with two parallel lines cut by a transversal the two outermost opposite angles
alternate interior angles
with two parallel lines cut by a transversal the two opposite inner angles
angle
the intersection of two noncollinear rays at a common endpoint. Rays are called sides and the endpoint called the vertex
angle bisector
a ray that divides an angle into two congruent angles
base angles
the four angles of a isosceles Trapezoid that are all congruent and the two congruent angles in an isosceles triangle
biconditional
the conjunction of a conditional statement and its converse
collinear
points that lie on the same plane
complementary angles
two angles with measures that have a sum of 90
congruence transformations
a mapping for which a geometric figure and its image are congruent. Examples include flip, slide, and turn
congruent
having the same measure
congruent triangles
triangles that have their corresponding parts congruent
conjecture
an educated guess based on known information
conjunction
a compound statement formed by joining two or more statements with the word and
consecutive interior angles
with two parallel lines cut by a transversal the inner same sided angles
contrapositive
the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.
converse
the statement formed by exchanging the hypothesis and conclusion of a conditional statement
coordinate proof
a proof that uses figures in the coordinate plane and algebra to prove geometric concepts
coplanar
points that lie in the same plane
corollary
a statement that can be easily proved using a theorem
corresponding angles
with two parallel lines cut by a transversal the angles that relate with one another and are congruent
counterexample
an example used to show that a given statment is not always true
deductive reasoning
a system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions
diagonals
in a polygon a segement that connects nonconsecutive vertices of the polygon
disjunction
a compound statement formed by joining two or more statements with the word or
equiangular triangle
a triangle with all angles congruent
equidistant
equal distance
equilateral triangle
a triangle with all sides congruent
exterior angle
an angle formed by one side of a triangle and the extension of another side
flow proof
a proof that organizes statements in logical order, starting with the given statements and using boxes and arrows
if-then statement
a compound statement of the form "if A, then B" where A and B are the statements
included angle
in a triangle the angle formed by two sides
included side
the sie of a triangle that is a side of each of two angles
inductive reasoning
reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction
inverse
the statement formed by negating both the hypothesis and conclusion of a conditional statement
isosceles trapezoid
a trapezoid in which the legs are congruent, both pairs of base angles are congruent, and the diagonals are congruent
isosceles triangle
a triangle with at least two sides congruent
kite
a quadrilateral with exactly two distinct pairs of adjacentn congruent sides
Law of Detachment
if p to q is a true conditional and p is true, then q is also true
Law of Syllogism
if p to q and q to r are true conditionals then p to r is also true
line segment
a measurable part of a line that consists of two points, called endpoints, and all of the points between them
linear pair
a pair of adjacent angles whose non-common sides are opposite rays
logically equivalent
statements that have the same truth values
median
In a trapezoid the segment that joins the midpoints of the legs
midpoint
the point halfway b/w the endpoints of a segment
negation
if a statement is represented by p, then this is not p of the statement
obtuse angle
an angle with degree measure greater than 90 but less than 180
obtuse triangle
a triangle with an obtuse angle
paragraph proof
an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true
parallel lines
coplanar lines that do not intersect
parallel planes
planes that do not intersect
parallelogram
a quadrilateral with parallel opposite sides
perimeter
the sum of the lengths of the sides of a polygon
perpendicular line
line that forms right angles
point-slope form
y-y1 = m(x-x1)
polygon
a closed figure formed by a finite number of coplanar segments called sides and the sides that have a common endpoint are noncollinear and each side intersects exactly two other sides, but only at their endpoints, called the vertices
postulate
a statement that describes a fundamental relationship b/w the basic terms of geometry. Accepted as true
rate of change
describes how a quantity is changing over time. Change in y over change in x to solve
ray
a part of a line that has one endpoint and extends indefinitely in one direction
rectangle
a quadrilateral with four right angles
remote interior angles
the angles of a triangle that are not adjacent to a given exterior angle
rhombus
a quadrilateral with all four sides congruent
right angle
an angle with the measure of 90 degrees
right triangle
a triangle with a right angle with opposite side the hypotenuse and the other two sides are legs
scalene triangle
a triangle with no two sides congruent
segment bisector
a segment, line, or plane that intersects a segment at its midpoint
skew lines
lines that do not intersect and are not coplanar
slope
change in y over change in x
slope-intercept form
y = mx + b
square
a quadrilateral with four right angles and four congruent sides
statement
any sentence that is either true or false, but not both
supplementary angles
two angles with measure that have a sum of 180
theorem
a statement/conjecture that can be proven true by undefined terms, definitions, and postulates
transversal
a line that intersects two or more lines in a plane at different points.
trapezoid
a quadrilateral with one pair of parallel sides.
truth table
a table used as a convenient method for organizing the truth values of statements
truth value
the truth/falsity of a statement
two-column proof
a formal proof that contains statements and reasons organized in two columns.
vertex angle
main angle in a triangle
vertical angles
two nonadjacent angles formed by two intersecting lines
Angle Addition Postulate
if R is in the interior of angle PQS then the m of PQR + m of RQS = m of PQS. and vice versa
Complement Theorem
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles
Supplement Theorem
if two angles form a linear pair, then they are supplementary angles
Vertical Angle Theorem
if two angles are vertical angles, then they are congruent
Alternate exterior angles Theorem
if two parallel lines are cut by a transversal, then each pair of alt exterior angles are congruent
Alternate Interior angles Theorem
if two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent
Corresponding angles Postulate
if two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent
Consecutive Interior Angles Theorem
if two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary
Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other
Parallel Postulate
if there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line
Angle Sum Theorem
the sum of the measures of hte angles of a triangle is 180
Third Angle Theorem
if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent
Angle Angle Side Theorem AAS
if two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle then the two triangles are congruent.
Exterior Angle Theorem
the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
Side Side Side Congruence SSS
if the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent
Side Angle Side Congruence SAS
if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then they are congruent
Angle Side Angle Theorem ASA
if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the two triangles are congruent.
Leg Leg Congruene LL
if the legs of one right triangle are congruent to the corresponding legs of another right triangle, they are congruent
Hypotenuse Angle Congruence HA
if the hypotenuse and acute angle of a right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then they are congruent
Leg Angle Congruence LA
If one leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then they are congruent
Hypotenuse Leg Congruence HL
if the hypotenuse and a leg of one right triangle are congruent to the same parts of another triangle then they are congruent
Interior Angle Sum Theorem
S = 180(n-2)
Exterior Angle Sum Theorem
sum equals 360
Reflexive Property of Congruence/Equality
r = r
Symmetric Property of Congruence/Equality
m = j, j = m
Transitive Property of Congruence/Equality
s = t, t = u, s = u
Properties of Parallelograms
Opposite sides and angles are congruent, consecutive angles are supplementary, if it has one right angle it has all right angles, diagonals bisect each other and separate it into two congruent triangles,
Properties of Quadrilaterals
if both pairs of opposite sides and angles are congruent then it is a parallelogram, if diagonals bisect each toehr and if one pair of opposite sides is parallel and congruent, then it is a parallelogram
Properties of Rectangles
All four angles are right angles, opposite sides are congruent and parallel, opposite angles are congruent, cons angles supplementary, diagonals congruent bisectors,
Properties of Rhombi
all the properties of parallelograms and quadrilaterals plus: The diagonals are perpendicular, each diagonal bisects a pair of opposite angles
Properties of Squares
all properites of parallelograms, quadrilaterals, rectangles and rhombi
Properties of Trapezoids
both pairs of base angles of an isosceles trapezoid are congruent as well as the diagonals, and the median is parallel to the bases and its measure is one half the sum of hte measures of the bases
Midpoint Theorem
if M is the midpoint of segment AB then segment AB is congruent to segment MB
Segment Addition Postulate
if B is b/w A and C then AB + BC = AC. converse also true
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