## 113 terms

figure in space

### line

figure that extends forever in two directions

### plane

figure that extends forever has no thickness

### space

set of all points

### collinear points

points all in one line

### coplanar points

points all in one plane

### intersection

set of points in two figures

### segment

figure with two endpoints of a line and all points in between

### ray

figure with an endpoint and extends in opposite direction

### opposite rays

two rays extending in opposite directions with the same endpoint

### length

distance between two points

### ruler postulate

points on a line can be in a coordinate system and the distance between any two points is the absolute value difference of their coordinates

if B is between A and C then AB + BC = AC

### congruent

two objects with the same shape and size

### congruent segments

segments with equal lengths

### segment midpoint

point which divides a segment in half

### segement bisector

midpoint intersector of a segment

### angle

figure formed by two rays with the same endpoint

angle rays

angle endpoint

measure 180

### protractor postulate

all angles on a protractor add up to 180 and any two rays make the measure of the angles by their absolute value difference

if B lies in the interior of <AOC then <AOB + <BOC = <AOC and if <AOC is 180 and B is not on AC then <AOB + <BOC = 180

two angles in a plane with a common vertex and side

### angle bisector

ray that divides angle into two congruent adjacent angles

### space postulate

line has two points, plane has three noncollinear points, and space has four noncoplanar points

### line postulate

only one line through any two points

### plane postulate

one plane through three points, only one plane through three noncollinear points

### line plane postulate

two points in a plane, line containing points is in plane

### intersect postulate

two planes intersect in a line

### intersect theorem

two lines intersect in a point and only one plane contains the lines

### line point theorem

only one plane through a line and point not on the line

### conditional

if then statement

### converse

reversed condtional

### inverse

negation of condtional

### contrapositive

negation of converse

### biconditional

conditional and converse are true

### midpoint theorem

M is AB midpoint, AM = 1/2AB and MB = 1/2AB

### angle bisector theorem

BX is <ABC bisector, <ABX =1/2<ABC and <XBC =1/2<ABC

### complementary

angles who equal 90

### supplementary

angles who equal 180

opposite angles

### vertical angle theorem

vertical angles are congruent

if two lines are perpendicular then they form congruent adjacent angles

### perpendicular line theorem

if two lines for congruent adjacent angles, the lines are perpendicular

### complementary angle theorem

if the exterior sides of two adjacent angles are perpendicular then angles are complementary

### supplement angle theorem

if two angles are supp of congruent angles then angles are congruent

### complement angle theorem

if two angles are comp of congruent angles then angles are congruent

### parallel lines

coplanar lines that do not intersect

### skew lines

noncoplanar lines

### parallel plane theorem

if two parallel planes are cut by a third plane then the lines of intersection are parallel

### corresponding angles postulate

if parallel lines are cut by transversal then corresponding angles are congruent

### AIA theorem

if parallel lines are cut by transversal then aia are congruent

### S-S interior angles theorem

if parallel lines are cut by transversal then s-s int angles are supplementary

### perpendicular transversal theorem

if transversal is perpendicular to one parallel line then it is perpendicular to the other parallel line

### perpendicular parallel theorem

in a plane two lines perpendicular to the same line are parallel

### perpendicular point theorem

through a point outside a line there is only one line perpendicular to the line

### parallel lines theorem

two lines parallel to a third line are parallel to each other

### scalene

triangle with no congruent sides

### isosceles

triangle with two congruent sides

### equilateral

triangle with all sides congruent

### equiangular

triangle with all angles congruent

### triangle theorem

sum of the angles in a triangle 180

### equiangular corollary

each angle of an equiangular triangle has measure 60

### right obtuse corollary

in a triangle there can only be one right or obtuse angle

### acute corollary

acute angles of a right triangle are complementary

### congruency corollary

if two angles of one triangle are congruent to a second triangle then the third angles are congruent

### exterior angle theorem

measure of an exterior angle of a triangle equals the sum of the two remote interior angles

### angle measure theorem

sum of the measures of the angles of a convex polygon with n sides is (n-2)180

### exterior sum theorem

sum of the measures of exterior angles in a convex polygon is 360

### SSS postulate

three sides of a triangle are congruent to three sides of another triangle then triangles are congruent

### SAS postulate

two sides and the included angles are congruent in two triangles, triangles are congruent

### ASA postulate

two angles and the included side are congruent in two triangles, triangles are congruent

### isosceles triangle theorem

two sides of a triangle are congruent then angles opposite the sides are congruent

### equilateral corollary

equilateral triangle is also equiangular

### isosceles bisector corollary

bisector o the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint

### opposite angle theorem

two angles of triangle are congruent then sides opposite angles are congruent

### AAS theorem

two angles and a nonincluded side of two triangles are congruent then the triangles are congruent

### HL theorem

hypotenuse and a leg of two right triangles are congruent then the triangles are congruent

### median

segment from a triangle vertex to midpoint of opposite side

### altitude

perpendicular segment from a triangle vertex to the line that contains the opposite side

### perpendicular bisector

line that is perpendicular to the segment at its midpoint

### perpendicular bisector theorem

if a point lies on the perpendicular bisector of a segment then the point is equidistant from the segment endpoints

### equidistant angle theorem

if a point on the bisector of an angle then the point is equidistant from the sides of the angle

### opposite sides theorem

opposite sides of a parallelogram are congruent

### opposite angles theorem

opposite angles of a parallelogram are congruent

### diagonal theorem

diagonals of a parallelogram bisect each other

### parallelogram side theorem

if one pair of opposite sides in a quadrilateral are both congruent and parallel then it is a parallelogram

### equidistant parallel theorem

if two lines are parallel then all points on one line are equidistant from the other line

### multiple transversal theorem

if three parallel lines cut of congruent segments on one transversal then they cut off congruent segments on all transversals

### triangle line theorem

line that contains the midpoint of one side of a triangle and is parallel to another side passes through the third side midpoint

### triangle segment theorem

segment that joins the midpoints of two sides of a triangle is parallel to and half as long as the third side

### parallelogram

quadrilateral with both pairs of opposite sides parallel

### square

quadrilateral with four congruent sides and right angles

### rectangle diagonal theorem

diagonals of a rectangle are congruent

### rhombus diagonal theorem

diagonals of a rhombus are perpendicular

### rhombus bisector theorem

each diagonal of a rhombus bisects two angles of the rhombus

### hypotenuse midpoint theorem

midpoint of the hypotenuse of a right triangle is equidistant from the three vertices

### rectangle theorem

if an angle of a parallelogram is a right angle then it is a rectangle

### rhombus theorem

if two consecutive sides of a parallelogram are congruent then it is a rhombus

### base angle theorem

base angles of an isosceles trapezoid are congruent

### trapezoid

quadrilateral with only one pair of parallel sides

parallel sides

### trapezoid median theorem

trapezoid median is parallel to the bases and has a length equal to the average of the base lengths

### exterior angle inequality theorem

measure of an exterior angle of a triangle is greater than the measure of either remote interior angle

### side inequality theorem

if one side of a triangle is longer than a second side then the angle opposite the first side is longer than the angle opposite the second side

### angle inequality theorem

if one angle in a triangle is larger than a second angle then the side opposite the first angle is larger then the side opposite the second angle

### perpendicular corollary

perpendicular segment from a point to a line or plane is the shortest segment from the point to the line or plane

### triangle inequality

sum of the lengths of any two sides of a triangle is greater than the length of the third side

### SAS inequality theorem

if two sides of two triangles are congruent but the included angle of the first triangle is larger than the second then the third side of the first triangle is longer than the third side of the second triangle

### SSS inequality theorem

if two sides of two triangles are congruent but the third side of the first triangle is longer than the second then the included angle of the first triangle is larger than the angle of the second