basic geometry adapted

What is Geometry?

-is the study of points, lines, angles,

surfaces, and solids.

BASIC TERMS

Point(s):

A point is a location in space. We may think of apoint as a "dot" on a piece of paper. We identify thispoint with a number or an upper case letter. A pointhas no length or width, it just specifies an exactlocation.

BASIC TERMS

Lines

A line is a collection of points that extendforever. We write the name of a line passing throughtwo different points A and F as "line AF" or as , thetwo-headed arrow over AF signifying a line passingthrough points A and F.

BASIC TERMS

Line Segment(s):

A line segment is part of a line. The following is asegment. A segment has two endpoints. A linesegment does not extend forever, but has twodistinct endpoints. We write the name of a linesegment with endpoints A and F as "line segmentAF" or as “FA” . Note how there are no arrow headson the line over AF such as when we denote a line ora ray.

BASIC TERMS

Ray(s):

A ray is a collection of points that begin at one point (an endpoint) and extend forever on one direction.The point where the ray begins is known as its endpoint. We write the name of a ray with endpoint A and passing through a point F as "ray AF". Note how the arrow head denotes the direction the ray extends in: there is no arrow head over the endpoint.

BASIC TERMS

Endpoint(s):

An endpoint is a point used to define a line segment or ray. A line segment has two endpoints; a ray has one.

BASIC TERMS

Plane:

A plane is a flat surface like a piece of paper. It extends in all directions. We can use arrows to show that it extends in all directions forever. The following is a plane.

BASIC TERMS

Parallel Line(s):

Two lines in the same plane which never intersect are called parallel lines. We say that two line segments are parallel if the lines that they lie on are parallel. If line 1 is parallel to line 2, we write this as line 1 || line 2

When two line segments DC and AB lie on parallel lines, we write this as segment DC || segment AB.

BASIC TERMS

Intersecting Lines

When lines meet in space or on a plane, we saythat they are intersecting lines The term intersectis used when lines, rays, line segments or figuresmeet, that is, they share a common point. The pointthey share is called the point of intersection.

ANGLE AND ANGLE TERMS

What is an Angle?Two rays that share the same endpoint

form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.


Here are some examples of angles.


We can specify an angle by using a point on each ray and the vertex. The angle below may be specified as angle ABC or as angle CBA; you may also see this written as ABC or as CBA. Note how the vertex point is always given in the middle.


Degrees: Measuring Angles We measure the size of an angle using degrees


Acute AnglesAn acute angle is an angle measuring between 0 and 90 degrees.


Obtuse AnglesAn obtuse angle is an angle measuring between 90 and 180 degrees.


Right AnglesA right angle is an angle measuring 90

degrees. Two lines or line segments that meet at a right angle are said to be perpendicular. Note that any two right angles are supplementary angles (a right angle is its own angle supplement).


Right Angles


Supplementary Angles

FIGURES and POLYGONS

Examples:

Understanding Volume

What is volume or capacity? In math, capacity is the amount a container will hold when full

Capacity is generally measured in milliliters, liters, or kiloliters. Take a look at the following container, which is a rectangular prism.

If the length, width, and height of this three-dimensional

container, measures 5 cm, 10 cm, and 20 cm respectively, the volume is 5 cm × 10 cm × 20 cm

= 1000 cm3

Surface Area

Surface AreaThe surface area of a space figure is the total area of all the faces of the figure.

SPACE FIGURES and BASIC SOLIDS

CubeA cube is a three-dimensional figure having six matching square sides.


CylinderA cylinder is a space figure having two congruent circular bases that are parallel.


CylinderThe figure picturedbelow is a cylinder.

The grayed lines are edges hidden from view.


SphereA sphere is a space figure having all of its points the same distance from its center. The distance from the center to the surface of the sphere is called its radius. Any cross-section of a sphere is a circle.


Sphere

basic geometry adapted

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