1.
A segment line or plane that intersects a segment at its midpoint.
Explanation
A bisector is a line or plane that intersects a segment at its midpoint. It divides the segment into two equal parts. In this case, a segment bisector is specifically referring to a line or plane that intersects a segment at its midpoint.
2.
In a right triangle, the sum of the square of the measures of the legs equals the square of the measure of the hypotenuse.
Explanation
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs). This theorem is a fundamental concept in geometry and is used to calculate unknown side lengths in right triangles. It allows us to understand the relationship between the sides of a right triangle and is widely applied in various fields such as architecture, engineering, and physics.
3.
Intersecting lines that form four right angles.
Explanation
The correct answer is "perpendicular" or "perpendicular lines" because when two lines intersect and form four right angles, they are considered perpendicular to each other. Perpendicular lines are a fundamental concept in geometry, and they are characterized by their right angles.
4.
An object consisting of two noncollinear rays with a common endpoint.
Explanation
An angle is a geometric shape formed by two noncollinear rays that share a common endpoint. In this case, the object described consists of two noncollinear rays with a common endpoint, which matches the definition of an angle. Therefore, the correct answer is "angle, an angle."
5.
If M is the midpoint of AB, then AM = MB.
Explanation
The midpoint theorem states that if M is the midpoint of AB, then AM = MB. This means that the distance from point A to M is equal to the distance from point M to B. This theorem is a fundamental concept in geometry and is used to prove various properties of triangles and other shapes. It is based on the idea that the midpoint of a line segment divides it into two equal parts.
6.
A boundless n-dimensional set of all points.
Explanation
The correct answer is "space, n-space." This refers to a boundless n-dimensional set of all points. In mathematics, "space" is a general term for a set of points, while "n-space" specifically refers to a set of n dimensions. Together, they represent an infinite set of points in n dimensions.
7.
Adjective describing a set of points, all of which lie on the same plane
Explanation
The term "coplanar" is an adjective used to describe a set of points that all lie on the same plane. In geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions. When all the points in a set lie on this same plane, they are considered coplanar. This term is often used to describe geometric figures or objects in space that can be represented by a flat surface.
8.
Unit of measure for angles.
Explanation
The unit of measure for angles is degree or degrees.
9.
A straight path connecting two points that can be extended indefinitely far in either direction.
Explanation
A line is a geometric figure that connects two points and extends infinitely in both directions. It is a straight path with no curves or bends. The terms "line" and "straight line" are used interchangeably to describe this concept.
10.
A set of points that are neither on the sides of the angle nor in the interior of the angle.
Explanation
The term "exterior" refers to a set of points that are neither on the sides of the angle nor in the interior of the angle. It can also be described as the space outside of the angle. Therefore, "exterior," "exterior of an angle," and "exterior of the angle" all correctly describe this concept.
11.
If Q is between P and R, then PQ + QR = PR,
orIf PQ + QR = PR, then Q is between P and R.
Explanation
The segment addition postulate states that if a point Q is between two points P and R on a line, then the sum of the lengths of PQ and QR is equal to the length of PR. In other words, if PQ + QR = PR, then Q is between P and R. This postulate is a fundamental concept in geometry that helps establish relationships between different segments on a line.
12.
The first coordinate in an ordered pair.
Explanation
The first coordinate in an ordered pair is commonly referred to as the x-coordinate or abscissa. It represents the horizontal position of a point on a graph or coordinate plane. This coordinate is often used in mathematical calculations and equations to determine the position or relationship between different points.
13.
If R is in the interior of ےPQS, then mےPQR + mےRQS = mےPQS
andIf mےPQR + mےRQS = mےPQS, then R is in the interior of ےPQS.
Explanation
The given answer is correct because it accurately identifies the concept being described in the question, which is the angle addition or angle addition postulate. This postulate states that if a point R is in the interior of angle PQS, then the sum of the measures of angle PQR and angle RQS will be equal to the measure of angle PQS. Similarly, if the sum of the measures of angle PQR and angle RQS is equal to the measure of angle PQS, then point R must be in the interior of angle PQS. Therefore, both statements are true and can be explained by the angle addition or angle addition postulate.
14.
The points that do not lie on the sides of an angle, but do lie on a line segment that connects the two sides of an angle.
Explanation
The points that do not lie on the sides of an angle, but do lie on a line segment that connects the two sides of an angle, are referred to as the interior of the angle.
15.
On a measured line, the midpoint of a segment
whose endpoints have the measures a and b is (a + b)/2
In a coordinate plane, the midpoint of a segment
with ends at (x_{1}, y_{1}) and (x_{2}, y_{2}) is at ((x_{1} + x_{2})/2, (y_{1} + y_{2})/2).
Explanation
The given answer "midpoint formulas, midpoint formula" is correct because it accurately describes the formulas used to find the midpoint of a segment on a measured line and in a coordinate plane. The first formula states that the midpoint of a segment on a measured line is equal to the average of the measures of its endpoints. The second formula states that the midpoint of a segment in a coordinate plane is equal to the average of the x-coordinates and the average of the y-coordinates of its endpoints. These formulas are commonly used to find the midpoint of a segment in geometry and coordinate geometry.
16.
A part of a line that extends indefinitely far in one direction.
Explanation
A ray is a part of a line that starts at a specific point and extends infinitely in one direction. It has no endpoint and continues indefinitely.
17.
Preposition to indictate the location of a point collinear with two points found in opposite directions.
Explanation
The preposition "between" is used to indicate the location of a point that is collinear with two points found in opposite directions. It suggests that the point is positioned in the middle or intermediate position between the two points.
18.
A flat surface that extends indefinitely far in all directions.
19.
Collinear rays in opposite directions defined by a common endpoint.
20.
The common endpoint of two rays that define an angle
21.
The commonly used horizontal number line
22.
Two angles, not necessarily adjacent, whose measures have a sum of 180.
23.
An angle whose measure is less than 90 degrees.
24.
The number of square units contained in the interior of a figure.
25.
The name of a point in the coordinate plane.
Explanation
An ordered pair is a combination of two numbers, denoted as (x, y), that represents the coordinates of a point in the coordinate plane. The first number, x, represents the horizontal position of the point, while the second number, y, represents the vertical position. By using ordered pairs, we can precisely locate and identify points in the coordinate plane.
26.
The postulate that says points on any line can be paired with real numbers such that, given any two points P and Q on the line, P corresponds to zero and Q corresponds to a positive number.
Explanation
The ruler postulate states that any line can be paired with real numbers, where one point on the line corresponds to zero and another point corresponds to a positive number. This means that every point on the line can be assigned a unique real number, creating a one-to-one correspondence between the points on the line and the real numbers.
27.
Euclidean geometric shapes that do not all lie in the same plane.
Explanation
The answer choices provided all describe shapes or figures that exist in three dimensions. "3d" is a commonly used abbreviation for "three-dimensional," and "3d shapes," "3d figures," "three dimensional," and "three dimensional figures" all refer to objects that have length, width, and height. These shapes do not all lie in the same plane, meaning they are not flat or two-dimensional.
28.
An angle whose measure is more than 90 degrees.
Explanation
An obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. It is larger than a right angle (90 degrees) but smaller than a straight angle (180 degrees). Therefore, the given answer "obtuse" is correct as it accurately describes an angle that is greater than 90 degrees in measure.
29.
The angle formed by two opposite rays.
Explanation
A straight angle is formed when two opposite rays line up in a straight line, creating a 180-degree angle. A linear angle is also formed by two opposite rays, but it can have any measure less than 180 degrees. Therefore, both straight angle and linear angle are correct answers for the given question.
30.
Adjective that describes a set of points because not all of them lie on the same line.
Explanation
The term "noncollinear" is used to describe a set of points that do not all lie on the same line. It indicates that the points are not in a straight line and are not collinear. This term is commonly used in geometry to describe points that are not connected in a linear fashion.
31.
A point M on line PQ between P and Q such that PM = MQ.
32.
Adjacent angles whose noncommon sides are opposite rays.
33.
The set of points common to two objects.
34.
An adjective describing a set of points all of which lie in the same plane.
Explanation
Coplanar is an adjective that describes a set of points that all lie in the same plane. This means that all the points in the set can be contained within a single flat surface. In other words, if you were to draw lines connecting any two points in the set, those lines would all lie within the same two-dimensional plane. Therefore, coplanar is the correct answer for this question.
35.
A unique location in space.
Explanation
The term "point" refers to a unique location in space. It is a fundamental concept in geometry and has no size or dimensions. A point is represented by a dot and is used to define the position of objects or describe the location of specific coordinates. It is the most basic element in spatial representation and serves as a building block for lines, shapes, and other geometric figures.
36.
The four regions divided by the x and y axes.
Explanation
The four regions divided by the x and y axes are called quadrants. Each quadrant represents a different combination of positive and negative values for the x and y coordinates. The first quadrant is located in the top right, the second quadrant in the top left, the third quadrant in the bottom left, and the fourth quadrant in the bottom right. The term "quadrant" is used to describe each individual region, while "quadrants" refers to all four regions together.
37.
Correspondence between a geometric object and a tool used for measuring such objects.
Explanation
This question is asking for a possible explanation for the correspondence between a geometric object and a tool used for measuring such objects. In this context, the terms "measure" and "measurement" are relevant because they are directly related to the act of quantifying the dimensions or attributes of a geometric object. Therefore, the correct answer is "measure, measurement."
38.
Two angles whose measures have a sum of 90.
Explanation
Complementary angles are two angles that add up to 90 degrees. In this case, the phrase "Two angles whose measures have a sum of 90" is describing complementary angles. The word "complements" is the verb form, indicating that the angles are complementing each other. "Complementary" is the adjective form, describing the relationship between the angles. "Complementary angles" is the noun form, referring to the specific type of angles that add up to 90 degrees.
39.
The name for the formula for the separation between any two points with coordinates (x_{1}, y_{1}) and (x_{2}, y_{2}) : d = √((x_{2 }- x_{1})^{2} + (y_{2} - y_{1})^{2})
Explanation
The given formula is commonly known as the distance formula. It is used to find the distance between two points in a coordinate plane. The formula calculates the distance by finding the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points. Therefore, the correct answer is distance formula.
40.
The distance around a figure.
Explanation
Perimeter and circumference both refer to the distance around a figure. Perimeter is typically used for two-dimensional figures, such as squares or rectangles, while circumference is specifically used for the distance around a circle. Therefore, both perimeter and circumference are correct answers to the question.
41.
Two nonadjacent angles formed by two intersecting lines.
Explanation
Vertical angles are formed when two lines intersect. They are opposite angles and are always congruent. In other words, the measure of one vertical angle is equal to the measure of its opposite vertical angle. This is a property of intersecting lines and can be observed in various geometric shapes and figures. Therefore, the correct answer is vertical angles.
42.
An angle whose measure is 90 degrees.
43.
Angles in the same plane that have a common vertex and a common side, but no common interior points.
44.
Name for the two rays that define an angle.
45.
Intersection of the x-axis and the y-axis.
Explanation
The origin is the point where the x-axis and the y-axis intersect. It is the point with coordinates (0,0) and serves as the reference point for the Cartesian coordinate system. All other points on the coordinate plane are located relative to the origin.
46.
The algebraic space for plotting points.
47.
The second coordinate in a numbered pair.
Explanation
The second coordinate in a numbered pair is commonly referred to as the y-coordinate or ordinate. In coordinate geometry, a numbered pair consists of an x-coordinate and a y-coordinate. The x-coordinate represents the horizontal position, while the y-coordinate represents the vertical position. Therefore, the correct answer includes "y," "y coordinate," and "ordinate" as all three terms are used to describe the second coordinate in a numbered pair.