97 terms

geometry

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two angles that add up to 90 degrees
complementary
points that lie on the same line
collinear
an angle whose measure is less than 90 degrees but greater than 0 degrees
acute
two angles in the same plane that have a common side and a common vertex but no interior points in common
adjacent
the union of two rays with a common endpoint
angle
a ray, segment, or line that goes through the vertex of a triangle and cutting the angle into two congruent angles
angle bisector
two angles whose sum is 180 degrees
supplementary
points that lie on the same plane
coplanar
the side of an isoceles triangle that is opposite the vertex angle
base
in an isoceles triangle, the angles formed by the base and one of the legs
base angle
an if-then statement is called a
conditional statement
two angles that have the same measure
congruent
a statement made by interchanging the hypothesis and conclusion of a conditional
converse
an example that shows a statement is false
counterexample
a triangle that has all three sides congruent
equilateral
a triangle that has one right angle
right triangle
a triangle that has all three angles congruent
equiangluar
a triangle that has three acute angles
acute triangle
a triangle that has one obtuse angle
obtuse triangle
an angle that is formed by extending one side of a triangle and its other side is a side of the triangle
exterior angle
a triangle with no congruent sides
scalene
an angle whose measure is greater than 90 degrees but les than 180 degrees
obtuse
an angle whose measure is 90 degrees
right
an angle whose measure is 180 degrees
straight
the side of a right triangle that is opposite the right angle
hypotenuse
reasoning that goes from specific examples to a general conclusion
inductive
reasoning that goes from general statements to specific examples
deductive
a triangle with at least two congruent sides
isosceles
a point that lies on a segment that divides the segment into two congruent segements
midpoint
a ray, line, or segment that goes through the midpoint of a segment
segment bisector
the angle of an isoceles triangle that lies between the two legs
vertex
a formal proof with statements on the left and reasons on the right that uses deductive reasoning
two column proof
a line that intersects two or more coplanar lines at different points
transversal
statement that must be proven to be true
theorem
a statement that is assumed true without proof
postulate
lines that lie in the same plane but do not intersect
parallel
lines that do not intersect and do not lie in the same plane
skew
lines that have exactly one point in common
intersecting
lines that have undefined slope
vertical
lines that have the same slope
parallel
lines that hav slope of 0
horizontal
lines that have slopes that are opposite recipricals of each other
perpendicular
the angles of a triangle that are not adjacent to the exterior angle
remote interior
lines that intersect and form right triangles
perpendicular
pair of angles made by intersecting lines that share only a common vertex and lie opposite of each other
vertical
a pair of adjacent angles whose exterior angle sides make a line
linear pair
the (blank) is the if part of a onditional that translates into the given information
hypothesis
the (blank) is the then part of a conditional that becomes the prove state of a proof
conclusion
~p is called the
negation
p-->q is called the
conditional
q-->p is caled the
converse
~p-->~q is called the
inverse
~q-->~p is called the
contrapositive
a (blank) is an educated guess
hypothesis
if p-->q is true then a specific p is true then q is ture. this is called
law of detachment
if p-->q and q-->r is true then p-->r is true. this is called
law of syllogism
it the 6 corresponding parts of two triangles are congruent then the triangles are
congruent
the (blank) of a polygon is the sum of the lengths of its sides
perimeter
the (blank) of a polygon is the number of square units it encloses
area
(blank) is the length around a circle
circumference
if point D lies in the interior of <ABC then the m<ABD + m<DBC = m<ABC. this is called the
angle addition postulate
if C is between A and B on a segment, then AC + CB = AB. this if called the
segment addition postulate
the intersection of two planes is a
line
through any two points there is exactly one
line
through any three noncollinear points there is exactly one
plane
a plane contains at least three (blank) points
noncollinear
a line contains at least two
points
if two points lie in a plane then the line containing those points li in the
same plane
through any point outside a line there is exactly (blank) line parallel to the given line through the given point
one
through a point outside a line there is exactly (blank) perpendicular to the given line through the given point
one
if two parallel lines are cut by a transversal, corresponding angles are
congruent
if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are
parallel
if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are
congruent
linear pairs are
supplementary
vertical angles are
congruent
all right angles are
congruent
supplements of the same angle are
congruent
complements of the same angle are
congruent
congruence of angles and segments are (blank), (blank), and (blank)
reflexive, symmetric, and transitive
if two parallel lines are cut by a transversal (blank) and (blank) angles are congruent
alternate exterior and alternate interior
it two parallel lines are but by a transversal, (blank) are supplementary
consecutive (same side) exterior and interior angles
if a transversal is perpendicular to one of two parallel lines, the it is (blank) to the other parallel line
perpendicular
in a plane two lines that are perpendicular to te same line are (blank) to each other
parallel
if two sides of a triangle are congruent then the angles opposite those sides are
congruent
if two angles of a triangle are congruent then the sides opposite those angles are
congruent
in a right triangle the square of the hypotenuse is equal to the sum of the squares of the legs. this is called the (blank) theorem
pythagorean
if two lines are cut by a transversal so that alternate interior or alternate exterior angles are congruent, then the lines are
parallel
if two lines are cut by a transversal so that sames side (consecutive) interior angles are supplementary then the lines are
parallel
the sum of the interior angles of a triangle is
180 degrees
the exterior angle of a triangle is equal to the sum of the (blank) of a triangle
two remote interior
an equiangular triangle is also
equilatral
each age of an equiangular triangle is (blank) degrees
60
if two angles of one triangle are congruent to two angles of another triangle then the third angles are
congruent
the acute angles of a right triangle are
complementary
in a triangle there cam be at most (blank) obtuse or right angle
one
list the ways to prove any two triangles congruent
sss, sas, asa, aas
list the way to prove right triangles congruent
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