97 terms

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

hl