Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which of the following definitions best describes the term "sector"?

1. A portion of a circle enclosed by two radii and an arc

2. A section defined by two chords intersecting at a point

3. A straight line splitting the circle into two equal halves

4. A curved line segment connecting points on the circumference

The correct answer is: A portion of a circle enclosed by two radii and an arc

The term "sector" in geometry refers specifically to a portion of a circle that is enclosed by two radii and the arc that connects the endpoints of those radii. This definition captures the essence of a sector by emphasizing both the linear boundaries formed by the radii and the curved boundary created by the arc. When considering a circle, visualizing a sector is akin to looking at a 'slice' of pizza, where the crust represents the arc and the two straight cuts leading to the center represent the radii. The other options describe different geometric elements. The second choice, which mentions two chords intersecting, does not align with the definition of a sector and instead relates to the concept of an intersection area within a circle. The third choice describes a diameter, which divides the circle into two equal halves but does not represent a sector. The fourth choice refers to a chord, which is a straight line connecting two points on the circumference, failing to account for the curved portion essential to the definition of a sector. Thus, the selection of the first option precisely encapsulates the characteristics of a sector within the context of circular geometry.