How Can You Name a Plane in Geometry
Geometry Fundamentals
Points, lines, and planes
Geometry originates from two Greek words: geos which ways world and metron which means measure. Information technology is a branch of mathematics that deals with the measurements of shape, sizes, relative positions of figures, and spatial properties. There are three fundamental concepts of geometry that are accepted without giving whatsoever articulate definition to it: the bespeak, the line, and the plane.
Terms to call up
| Clockwise | - a motion that proceeds in the same direction as a clock'due south hand: from pinnacle to correct, then down and so left. |
| Counter clockwise | - a movement that gain in the opposite direction as a clock'southward hands: from top to left, then down and and so right. |
| Dimension | - a measure out of extent or magnitude such every bit length, width and top. |
| Noncollinear | - does not lie on the same line. |
| Straight | - directly, non bend or without a bend. |
Point
A indicate refers to a location or position. It has no dimensions since it has no length, width, or pinnacle. Points are used to identify the position of a sure object from a standard arbitrary signal. A point is ordinarily labeled with an uppercase letter. Effigy ane shows a three point labeled every bit A, B, and C.
Example 1:
In the figure below, what is the leftmost signal?
G
Explanation:
The point at the leftmost side is labeled with Thousand.
Example two:
Find the point nearest to R in the figure shown.
South
Explanation:
The betoken labeled with South is the nearest to the point labeled with R.
Line
A line is a set of all points that extend continuously on either of its direction. It is infinite, straight, and one-dimensional. A line tin can exist identified by naming two points that lie on it and describe a line ( ) over the letters which indicate the proper noun of each indicate. It can likewise be named past a single lowercase letter. Figure ii shows two lines labeled as (FG) and m.
Example three:
Proper name the line beneath.
(CP) or (PC)
Explanation:
Points C and P lie on the prevarication and therefore their labels can exist used as the name of the line. Since the arrangement of the letters is considerable, information technology can be CP or PC. So put a line sign ( ) over the letters.
Example four:
How many means tin you proper name the line in the given?
seven
Explanation:
Using the points that prevarication on it, the line can be labeled equally (XY), (YX), (XZ), (ZX), (YZ), and (ZY).
The line tin can also be named using the lowercase letter t.
Therefore, the line in the given to a higher place can be named in 7 ways.
Example 5:
Draw (UV).
vii
Explanation:
Draw two points and characterization it as U and V.
Connect the two points straight at each other and extend the line.
Depict an arrowhead on both ends of the line.
Airplane
A plane is a flat surface having two dimensions extending indefinitely. Information technology has a length and a width. It can be identified by determining 3 noncollinear points. Information technology is labeled according to the letters used to label the points and the fashion should exist either in clockwise or counterclockwise management. Figure 3 shows 2 planes JKL and MNOP.
Instance 6:
What is the name of the aeroplane given?
Aeroplane PLN, PNL, LPN, LNP, NLP, or NPL
Caption:
Consider P, L, and N as points that lie in the airplane.
Use their labels as the name of the plane.
In clockwise direction, the plane tin can be named equally PNL, NLP, or LPN.
In counterclockwise direction, the plane can be named as PLN, LNP, or NPL.
Instance 7:
Detect the number of ways to label the plane beneath.
8
Explanation:
Consider N, A, M, and E as points that lie in the aeroplane.
Use their labels as the name of the plane.
In clockwise direction, the aeroplane can exist named as NAME, AMEN, MENA, or ENAM.
In counterclockwise management, the aeroplane can be named as NEMA, EMAN, MANE, or ANEM.
Therefore, the plane can be labeled in 8 ways.
Example eight:
Draw plane STAR.
Explanation:
Depict four points and characterization them as S, T, A, and R.
Connect points S and T straight at each other.
Connect points T and A direct at each other.
Connect points A and R straight at each other.
Connect points R and Due south direct at each other.
Source: https://www.ipracticemath.com/learn/geometry/points-lines-planes
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