A) Precisely define an angle. (1 point)

Question

An angle is the figure formed by two lines extending from the same point.
An angle is the finite section of a line between two endpoints on the line.
An angle is a closed plane curve with every point on the curve equidistant from a fixed point
within the curve.
An angle is a line that extends forever in one direction for a single endpoint.

Answer 1

The correct definition of an angle from the options provided is:

An angle is the figure formed by two lines extending from the same point.

This accurately describes an angle as it comprises two rays (or line segments) that share a common endpoint, known as the vertex of the angle.

Answer 2

A) What makes a line parallel? (1 point)
A parallel line is a line that intersects another line at a 90-degree angle.
A parallel line is a straight line that always remains the same distance from another line and
never intersects it.
A parallel line is a straight figure that has no thickness and extends infinitely in two opposite
directions.
A parallel line is the finite section of a line between two points on that line.

Answer 3

The correct statement that defines what makes a line parallel is:

A parallel line is a straight line that always remains the same distance from another line and never intersects it.

This defines parallel lines as lines that do not meet, regardless of how far they are extended.

Answer 4

A) Which of the following is an example of an undefined notion? (1 point)
A circle is an undefined notion.
A line is an example of an undefined notion.
An angle is an example of an undefined notion.
A line segment is an example of an undefined notion.

Answer 5

The correct example of an undefined notion from the options provided is:

A line is an example of an undefined notion.

In geometry, a line is typically considered an undefined term, as it is fundamental to the subject and is not formally defined using other terms. Instead, it is understood through its properties and how it relates to other concepts.

Answer 6

A) Postulates, definitions, conjectures, and theorems each have distinguishing features that
help identify them. Which of the following answer choices accurately represents the term’s
distinguishing feature? (1 point)
A theorem is assumed to be true, and it does not have to be proven.
A postulate is assumed to be true, and it does not have to be proven.
A definition is a statement that is made based on observations that must be proven true.
A conjecture tells you what a term means or what to do with a concept.

Answer 7

The correct statement that accurately represents the distinguishing feature of the term is:

A postulate is assumed to be true, and it does not have to be proven.

In the context of mathematics and geometry, a postulate (or axiom) is a foundational statement accepted as true without proof.

Answer 8

A) The building blocks of geometry are the undefined terms of point, line, plane, and space.
Which of the undefined terms has no dimension? (1 point)
a line
a point
a plane
space

Answer 9

The undefined term that has no dimension is:

a point.

A point is defined as a location in space that has no length, width, or height—therefore, it is considered to have no dimensions.