Tools of Geometry Chapter 1 Vocabulary Mrs. Robinson

Objective Chapter 1 Vocabulary Tools of Geometry

Essential Questions How can I use vocabulary in the real world?

Undefined term The most basic figures in geometry which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

point has no dimension. It is usually represented by a small dot

line A straight path that has no thickness and extends forever two arrowheads to indicate that the line extends without end in two directions.

plane A flat surface that has no thickness and extends forever

collinear Points that lie on the same line K, L, and M are collinear K

coplanar Points that lie on the same plane. Otherwise they are noncoplanar. Name four coplanar points A, B, C, D

segment Or line segment The part of a line consisting of two points and all points between them.

endpoint A point at one end of a segment or the starting point of a ray

ray Consists of the initial point 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 or axiom a statement or rules that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

Postulate or axiom pg. 14

Postulate or axiom pg. 20

coordinate The real number that corresponds to a point See postulate 1-5 on pg. 20

distance absolute value of the difference of the coordinates. AB = |a – b| or |b - a| A a B b

length The distance between A and B is also called the length of AB, or AB. AB = |a – b| or |b - a| A a B b

construction a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge. Sketch, draw, and construct a segment congruent to MN.

between all three points must lie on the same line, and AB + BC = AC.

congruent segments Segments that have the same length

midpoint pg. 23 A point on a line segment that divides it into two equal parts The halfway point of a line segment

Midpoint formula

bisect To divide into two equal parts. You can bisect lines, angles, and more. The dividing line is called the "bisector"

segment bisector pg.23 A line, ray or segment which cuts another line segment into two equal parts.

angle consists of two different rays that have the same initial point. You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

vertex A point where two or more straight lines meet. A corner. plural: vertices

interior of an angle an angle between points that lie on each side of the angle.

exterior of an angle an angle not on the angle or in its interior.

measure the absolute value of the difference of the real numbers paired

degree A measure for angles. There are 360 degrees in a full rotation. The symbol for degrees is ° Example: 90 degrees (90°) is a right angle.

acute angle An angle less than 90° (90° is called a Right Angle)

right angle An angle which is equal to 90°, one quarter of a full revolution

obtuse angle An obtuse angle is one which is more than 90° but less than 180° In other words, it is between a right angle and a straight angle.

straight angle A straight angle changes the direction to point the opposite way. It looks like a straight line. It measures 180° (half a revolution, or two right angles)

Types of Angles pg. 30

congruent angle angles that have the same measure. The Angle Addition Postulate is very similar to the Segment Addition Postulate

angle bisector A line that splits an angle into two equal angles. ("Bisect" means to divide into two equal parts.)

adjacent angles Two angles in the same plane with a common vertex and a common side, but no common interior points.

linear pair Two adjacent angles whose noncommon sides are opposite rays. The angles of a linear pair form a straight angle

complementary angles Two angles are if the sum of their measures is 90°

supplementary angles Two angles are if the sum of their measures is 180°

vertical angles Two angles are if their sides form two pairs of opposite rays.

perimeter P of a plane figure is the sum of the side lengths of the figure. Measured in single units

area A of a plane figure is the number of non- overlapping square units of a given size that exactly cover the figure. Measured in square units

Perimeter & Area

base The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle.

height The vertical distance from top to bottom

diameter a segment that passes through the center of the circle and whose endpoints are on a circle.

radius a segment whose endpoints are the center of the circle and a point on the circle.

circumference Distance around a circle. Measured in single units

pi (𝜋) 3.14159265359 ………………….. The ratio of a circle’s circumference to its diameter is the same for all circles. This ratio is represented by the Greek letter  (pi). The value of  is irrational. Pi is often approximated as 3.14 or .

Circumference and Area of a Circle The circumference C of a circle is given by the formula 𝑪=𝝅𝒅 or 𝑪=𝟐𝝅𝒓 The area A of a circle is given by the formula 𝑨=𝝅𝒓𝟐

coordinate plane a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) . The location, or coordinates, of a point are given by an ordered pair (x, y).

leg In a right triangle, the two sides that form the right angle

hypotenuse The side across from the right angle that stretches from one leg to the other In other words, the longest side of a triangle.

transformation a change in the position, size, or shape of a figure

preimage The original figure

image The resulting figure

Example of preimage & image

reflection Or flip A transformation across a line, called the line of reflection. Each point and its image are the same distance from the line of reflection

rotation Or turn A transformation about a point P, called the center of rotation. Each point and its image are the same distance from P

translation Or slide A transformation in which all the points of a figure move the same distanced in the same direction.