Question

Which undefined term is used to define an angle ?

Answer 1

Point.

Further explanation

• This is one of the classic problems of Euclidean geometry.
• The angle is determined by three points, we call it A, B, C, with A ≠ C and B ≠ C.  
• We express an angle with three points and a symbol ∠. The middle point represents constantly vertex. We can, besides, give angle names only with vertices. For example, based on the accompanying image, the angle can be symbolized as ∠BAC, or ∠CAB, or ∠A.  

Types of Angles  

• The acute angle represents an angle whose measure is greater than 0° and less than 90°.
• The right angle is an angle that measures 90° precisely.  
• The obtuse angle represents an angle whose measures greater than 90° and less than 180°.  
• The straight angle is a line that goes infinitely in both directions and measures 180°. Carefully differentiate from rays that only runs in one direction.

Note:

Undefined terms are the basic figure that is undefined in terms of other figures. The undefined terms (or primitive terms) in geometry are a point, line, and plane.

These key terms cannot be mathematically defined using other known words.

• A point represents a location and has no dimension (size). It is marked with a capital letter and a dot.
• A line represent an infinite number of points extending in opposite directions that have only one dimension. It has one dimension. It is a straight path and no thickness.
• A plane represents a planar surface that contains many points and lines. A plane extends infinitely in all four directions. It is two-dimensional. Three noncollinear points determine a plane, as there is exactly one plane that can go through these points.  

Learn more  

1. Undefined terms are implemented to define a ray brainly.com/question/1087090
2. Definition of the line segment brainly.com/question/909890  
3. What are three collinear points on a line? brainly.com/question/5795008  

Keywords: the definition of an angle, the undefined term, line, point, line, plane, ray, endpoint, acute, obtuse, right, straight, Euclidean geometry

Answer 2

The undefined term which is used to define an angle is line i.e., $\fbox{\begin\\\ option A\\\end{minispace}}$.

Further explanation:

In geometry the three terms which are considered to be undefined are line, point and plane. From these three undefined terms the other terms in the geometry are defined.

A point represents a location in space and a point has no dimension i.e., a point has no length, no width and no height.

In the Cartesian plane a point is represented as an ordered pair as $(x,y)$.

A line is a one dimensional figure which has infinite length, no width and no height. A line extends in both the direction infinitely and line is also defined as a collection of infinite number of points in such a way that all the points lies straight one after another.

A plane is a two dimensional figure which has infinite length, infinite width and no height. A plane extends infinitely in all the directions.

Figure 1 (attached in the end) shows a point, a line and a plane.

As per the given options, option D as ray is incorrect because ray is not considered as an undefined term in the geometry so, option D is discarded.

A ray is defined as a line which starts from one point and the other end extends infinitely. A ray has one end point.

If we start from zero dimension i.e., a point because a point represents just a location in space which has no length and no width.

From the term point the term angle cannot be defined because a point represents a location and an angle is not a location.

This implies that the option C is incorrect.  

For one dimension i.e. a line because a line is a one dimensional figure which has infinite length, no width and no height.

From the term line the term angle can be defined because when two lines intersect at a point an angle is formed.

An angle is defined as a figure which is formed when two lines intersect each other at a point.

Figure 2 (attached in the end) shows the formation of an angle when two lines intersect each other at one point.

This implies that the term angle is defined from the undefined term line.

So, the option A is correct.

For two dimension i.e., a plane which is a two dimensional figure with infinite length, infinite width and no height.

From the undefined term plane the term angle cannot be defined.

This implies that the option B is incorrect.

Therefore, the undefined term which is used to define the term an angle is line.

Thus, the undefined term which is used to define an angle is line i.e., $\fbox{\begin\\\ option A\\\end{minispace}}$.

Learn more:

1. A problem to determine the equation of the line brainly.com/question/5337932

2. A problem to determine the point slope form of line brainly.com/question/4097107

3. A problem to determine range of the function brainly.com/question/1435353

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Geometry

Keywords: Geometry, lines, angles, plane, ray, point, undefined term, space, plane, Cartesian plane, dimension, collinear, Euclidean geometry.