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Geometry Ch. 1

Foundations for Geometry- vocabulary

TermDefinition
undefined term a basic figure that is not defined in terms of other figures: point, line, plane
point (an undefined term in geometry) it names a location and has no size
line (an undefined term in geometry) a straight path that has no thickness and extends forever
plane (an undefined term in geometry) a flat surface that has no thickness and extends forever
collinear points that lie on the same line
coplanar points that lie on the same plane
segment of a line a part of a line consisting of two endpoints and all points between them
endpoint a point at an end of a segment of the starting point of a ray
ray a part of a line that starts at an endpoint and extends forever in one direction
opposite rays two rays that have a common endpoint and form a line
postulate (also called an axiom) a statement that is accepted as true without proof
Postulate 1-1-1 Through any two points there is exactly one line.
Postulate 1-1-2 Through any three noncollinear points there is exactly one plane containing them.
Postulate 1-1-3 If two points lie in a plane, then the line containing those points lies in the plane.
Postulate 1-1-4 If two lines intersect, then they intersect in exactly one point.
Postulate 1-1-5 If two planes intersect, then they intersect in exactly one line.
coordinate a number used to identify the location of a point
distance between two points the absolute value of the difference of the coordinates of the points
length the distance between the two endpoints of a segment
congruent segments two segments that have the same length
construction a method of creating a figure that is considered to be mathematically precise; uses a compass and straightedge, geometry software, or paper folding
between Given three points A, B, and C, B is between A and C if and only if all three of the points lie on the same line, and AB + BC = AC.
midpoint the point that divides a segment into two congruent segments
bisect to divide into two congruent parts
segment bisector a line, ray, or segment that divides a segment into two congruent segments
Ruler Postulate (1-2-1) The points on a line can be put into a one-to-one correspondence with the real numbers.
Segment Addition Postulate (1-2-2) If B is between A and C, then AB + BC = AC.
angle a figure formed by two rays with a common endpoint
vertex of an angle the common endpoint of the sides of the angle
interior of an angle the set of all points between the sides of an angle
exterior of an angle the set of all points outside an angle
degree a unit of angle measure (1/360 of a circle)
acute angle an angle that measures greater than 0º and less than 90º
right angle an angle that measures 90º
obtuse angle an angle that measures greater than 90º and less than 180º
straight angle a 180º angle
congruent angles angles that have the same measure
angle bisector a ray that divides an angle into two congruent angles
Protractor Postulate (1-3-1) Given line AB and a point O on line AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180.
Angle Addition Postulate (1-3-2) (∠ Add. Post.) If S is the in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR.
adjacent angles two angles in the same plane with a common vertex and a common side but no common interior points
linear pair a pair of adjacent angles whose noncommon sides are opposite rays (form a straight line)
complementary angles two angle whose measures have a sum of 90º
supplementary angles two angles whose measures have a sum of 180º
vertical angles the nonadjacent angles formed by two intersecting lines
perimeter (definition) the sum of the sides lengths of a close plane figure
area (definition) the number of nonoverlapping unit squares of a given size that will exactly cover the interior of a plane figure
base of a triangle any side of a triangle
height of a triangle a segment from a vertex that forms a right angle with a line containing the base
diameter a segment that has endpoints on the circle and that passes through the center of the circle
radius of a circle a segment who endpoints are the center of a circle and a point on the circle
circumference (definition) the distance around the circle
pi (π) the ratio of the circumference of a circle to its diameter, ≈ 3.14...
coordinate plane a plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis
leg of a right triangle one of the two sides of the right triangle that form the right angle
hypotenuse the side opposite the right angle in a right triangle
Pythagorean Theorem (Thm 1-6-1) In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (a^2 + b^2 = c^2)
transformation a change in the position, size, or shape of a figure or graph
preimage the original figure in a transformation
image a shape that results from a transformation of a figure known as the preimage
reflection a transformation across a line such that the line of reflection is the perpendicular bisector of each segment joining each point and its image
rotation a transformation about the point P such that each point and its image are the same distance from P
translation a transformation that shifts or slides every point of a figure or graph the same distance in the same direction
congruent having the same size and shape, denoted by ≅
Pythagorean Triples a set of three nonzero whole numbers that satisfy the Pythagorean Theorem (such as {3,4,5}, {5,12,13}, or {7,24,25})
Created by: rivey