Points, Lines, and Planes Quick Check 1 of 51 of 5 Items Question Precisely define an angle.(1 point) Responses 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 closed plane curve with every point on the curve equidistant from a fixed point within the curve. An angle is the finite section of a line between two endpoints on the line. An angle is the finite section of a line between two endpoints on the line. An angle is a line that extends forever in one direction for a single endpoint. An angle is a line that extends forever in one direction for a single endpoint. An angle is the figure formed by two lines extending from the same point. An angle is the figure formed by two lines extending from the same point.

Answer 1

The correct response is: An angle is the figure formed by two lines extending from the same point.

This definition captures the essence of an angle, which consists of two rays (or line segments) that share a common endpoint, known as the vertex of the angle.

Answer 2

Points, Lines, and Planes Quick Check 2 of 52 of 5 Items Question What makes a line parallel?(1 point) Responses 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 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 a straight figure that has no thickness and extends infinitely in two opposite directions. A parallel line is a line that intersects another line at a 90-degree angle. A parallel line is a line that intersects another line at a 90-degree angle. A parallel line is the finite section of a line between two points on that line.

Answer 3

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

This definition accurately describes the property of parallel lines, which is that they do not meet and maintain a constant distance apart.

Answer 4

Points, Lines, and Planes Quick Check 3 of 53 of 5 Items Question Which of the following is an example of an undefined notion?(1 point) Responses An angle is an example of an undefined notion. An angle is an example of an undefined notion. A circle is an undefined notion. A circle is an undefined notion. A line segment is an example of an undefined notion. A line segment is an example of an undefined notion. A line is an example of an undefined notion. A line is an example of an undefined notion.

Answer 5

The correct response is: A line is an example of an undefined notion.

In geometry, undefined terms are foundational concepts that are not formally defined using other concepts. Lines, points, and planes are common examples of such undefined notions, as they form the basis for other geometrical definitions and theorems.

Answer 6

Points, Lines, and Planes Quick Check 4 of 54 of 5 Items Question 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) Responses A postulate 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 conjecture tells you what a term means or what to do with a concept. A conjecture tells you what a term means or what to do with a concept. A theorem is assumed to be true, and it does not have to be proven. A theorem 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.

Answer 7

The correct response is: A postulate is assumed to be true, and it does not have to be proven.

This accurately describes the distinguishing feature of a postulate. Postulates (or axioms) are accepted as true without proof in the framework of a mathematical system. The other definitions provided in the options do not correctly represent the terms they reference.