Chapters 3-4 Flashcards
lines that do not intersect and are not coplanar
skew lines
coplanar lines that do not intersect
parallel lines
planes that do not intersect
parallel planes
a line that intersects 2 or more coplanar lines at 2 different points
transversal
the angles on the inside of the transversal pair of angles
interior anges
angles on the outside of the transversal pair of angles
exterior angles
interior angles that lie on the same side of he transversal
consecutive interior angles
nonadjacent interior angles that lie on opposite sides of the transversal
alternate interior angles
nonadjacent exterior angles that lie on the opposite sides of the transversal
alternate exterior angles
angles that lie on the same side of the transversal and on the same side of 2 lines
corresponding angles
if two parallel lines are cut by a transversal then each pair of corresponding angles is congruent
corresponding angles postulate
if two parallel angles are cut by a transversal, then each pair of alternate interior angles is congruent
alternate interior angles theorem
if two parallel lines are cut b a transversal then exactly one pair of consecutive interior angles is supplementary
consecutive interior angles theorem
the ratio of the change along the y-axis to the change along the x-axis between any two points on the line
rise over run
slope
describes how a quantity y changes in relation to quantity x
rate of change
two non-vertical lines have the same slope if and only if hey are parallel
all vertical lines are parallel
slopes of parallel lines
two non-vertical lines are perpendicular if and only if the product of their slopes is -1, vertical lines are perpendicular
slopes of perpendicular lines
y=mx+b
where m is the slope of the line and b is the y-intecept
slope-intercept form
y-y1=m(x-x1)
where (x1, y1) is any point on the line and m is the slope of the line
point-slope form
the equation of this term is y=b where b is the y-intercept of the line
horizontal line equation
the equation of this term is x=a where a is the x-intercept of the line
vertical line equation
if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
converse of corresponding angles postulate
if given 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
parallel postulate
if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
alternate exterior angles converse
if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
consecutive interior angles converse
if two lines in a plane are cut by a transversal so that a pair f alternate interior angles is congruent, then the lines are parallel
alternate interior angles converse
in a plane, if two lines are perpendicular to the same line, then they are parallel
perpendicular transversal converse
if given a line and a point not on the line, then there exists exactly one line through the point that is perpendicular to the given line
perpendicular postulate
the distance between two lines measured along a perpendicular line to the lines is always the same
equidistant
a triangle with three acute angles
acute triangle
a triangle with three congruent angles
equiangular triangle
a triangle with one obtuse angle
obtuse triangle
a triangle with one right angle
right triangle
a triangle with three congruent sides
equilateral triangle
a triangle with at least two congruent sides
isosceles triangle
a triangle with no congruent sides
scalene triangle
the sum of the measures of the angles of a triangle is 180
triangle angle-sum theorem
an extra line or segment drawn in a figure to help analze geometric relationships
auxiliary line
angles formed by one side of the triangle and the extension of an adjacent side
exterior angles
each exterior angle of a triangle has two of these that are not adjacent to the exterior angle
remote interior angles
the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
exterior angles theorem
this term uses statements written in boxes and arrows to show the logical progression of an argument
flow proof
a theorem with a proof that follows as a direct result of another theorem
corollary
the acute angles of a right triangle are complementary
there can be at most one right or obtuse angle in a triangle
triangle angle-sum corollaries
if two geometric figures have exactly the same shape and size then they are this
congruent
all of the parts of one polygon are congruent to the corresponding angles
congruent polygons
matching parts of the other polygon
include corresponding angles and corresponding sides
corresponding parts
two polygons are congruent if and only if their corresponding parts are congruent
definition of congruent polygons
if two angles of one triangle are congruent to the angles of a second triangle, then the third angles of the triangles are congruent
third angles theorem
if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent
side-side-side (SSS) congruence
if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent
side-angle-side (SAS) congruence
the side located between two consecutive angles of a polygon
included side
if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
angle-side-angle (ASA) congruence
if two angles and the non-included side of one triangle are congruent tot he corresponding two angles and side of a second triangle, then the two triangles are congruent
angle-angle-side (AAS) congruence
the two congruent sides of an isosceles triangle
legs of an isosceles triangle
the angle with sides that are the legs is called this
vertex angle
the two angles formed by the base and the congruent sides are called this
base angles
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
isosceles triangle theorem
if two angles of a triangle are congruent, then the sides opposite those angles are congruent
converse of isosceles triangle theorem
a triangle is equilateral if and only if it is equiangular
each angle of an equilateral triangle measures 60
equilateral triangle
an operation that maps an original geometric figure, the preimage, onto a new figure called the image
transformations
an original geometric figure
preimage
a new figure
image
a rigid transformation is one in which the position of he image may differ from that of the preimage, but the two figures remain congruent
congruence transformation
a rigid transformation
isometry
a transformation over line called the line of reflection
each point of the preimage and its image are the same distance from the line of reflection
reflection or flip
a transformation that moves all points of the original figure the same distance in the same direction
translation or slide
a transformation around a fixed point called the center of rotation, through a specific angle, and in a specific direction
each point of the original figure and its image are the same distance from the center
rotation or turn
figures in the coordinate plane an algebra to prove geometric concepts
coordinate proofs
