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