Vocabulary 1: Points, Lines & Planes

Submit

2) An adjective describing a set of points all of which lie in the same plane.

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.

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.

Submit

3) A unique location in space.

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.

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.

Submit

4) The four regions divided by the x and y axes.

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.

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.

Submit

5) Correspondence between a geometric object and a tool used for measuring such objects.

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."

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."

Submit

6) Two angles whose measures have a sum of 90.

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.

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.

Submit

7) The name for the formula for the separation between any two points with coordinates (x₁, y₁) and (x₂, y₂) : d = √((x₂- x₁)² + (y₂ - y₁)²)

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.

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.

Submit

8) The distance around a figure.

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.

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.

Submit

9) Two nonadjacent angles formed by two intersecting lines.

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.

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.

Submit

13) Intersection of the x-axis and the y-axis.

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.

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.

Submit

15) The second coordinate in a numbered pair.

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.

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.

Submit

16) A segment line or plane that intersects a segment at its midpoint.

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.

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.

Submit

17) In a right triangle, the sum of the square of the measures of the legs equals the square of the measure of the hypotenuse.

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.

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.

Submit

18) Intersecting lines that form four right angles.

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.

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.

Submit

19) An object consisting of two noncollinear rays with a common endpoint.

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."

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."

Submit

20) If M is the midpoint of AB, then AM = MB.

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.

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.

Submit

21) A boundless n-dimensional set of all points.

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.

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.

Submit

22) Adjective describing a set of points, all of which lie on the same plane

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.

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.

Submit

24) A straight path connecting two points that can be extended indefinitely far in either direction.

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.

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.

Submit

25) A set of points that are neither on the sides of the angle nor in the interior of the angle.

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.

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.

Submit

26) If Q is between P and R, then PQ + QR = PR, or

If PQ + QR = PR, then Q is between P and R.

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.

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.

Submit

27) The first coordinate in an ordered pair.

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.

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.

Submit

28) If R is in the interior of ےPQS, then mےPQR + mےRQS = mےPQS and If mےPQR + mےRQS = mےPQS, then R is in the interior of ےPQS.

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.

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.

Submit

29) 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.

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.

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.

Submit

30) 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 (x₁, y₁) and (x₂, y₂) is at ((x₁ + x₂)/2, (y₁ + y₂)/2).

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.

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.

Submit

31) A part of a line that extends indefinitely far in one direction.

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.

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.

Submit

32) Preposition to indictate the location of a point collinear with two points found in opposite directions.

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.

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.

Submit

40) The name of a point in the coordinate plane.

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.

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.

Submit

41) 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.

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.

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.

Submit

42) Euclidean geometric shapes that do not all lie in the same plane.

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.

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.

Submit

43) An angle whose measure is more than 90 degrees.

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.

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.

Submit

44) The angle formed by two opposite rays.

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.

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.

Submit

45) Adjective that describes a set of points because not all of them lie on the same line.

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.

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.

Submit