Math Chapter 7 Lessons 1-4

A point in geometry is a precise location in space with no size, typically represented as a dot. It has no length, width, or height. Lines, planes, and circles are all geometric shapes that have dimension and are not just a single point in space.

A line is a one-dimensional geometric figure that extends infinitely in opposite directions. It has no endpoints. A ray has one endpoint and extends infinitely in one direction. A line segment has two endpoints. A curve does not extend infinitely in opposite directions.

A ray is a part of a line that has one endpoint and extends infinitely in one direction. A line has no endpoints, a line segment has two endpoints, and a vector typically has both magnitude and direction.

A plane is a two-dimensional flat surface that extends infinitely in all directions.

In geometry, figures that have the same shape and size are referred to as congruent. 'Similar' refers to figures that have the same shape but not necessarily the same size. 'Identical' implies that the figures are exactly the same in both shape and size. 'Equivalent' is a term used in mathematics to indicate that two expressions or values are equal.

An angle is formed when two rays have a common endpoint, while a line is formed by a collection of points extending infinitely in both directions, a circle is a set of all points equidistant from a center point, and a polygon is a closed figure made up of line segments.

In graph theory, the common endpoint in a graph is referred to as a vertex, which is represented by a point where edges intersect.

A right angle is formed when two lines are perpendicular to each other, measuring exactly 90 degrees. An acute angle measures less than 90 degrees, an obtuse angle measures more than 90 degrees but less than 180 degrees, and a straight angle measures exactly 180 degrees.

An acute angle is any angle that measures less than 90 degrees. A right angle measures exactly 90 degrees, an obtuse angle measures between 90 and 180 degrees, and a straight angle measures exactly 180 degrees.

An obtuse angle is greater than 90 degrees and less than 180 degrees. An acute angle is less than 90 degrees, a right angle is exactly 90 degrees, and a straight angle is exactly 180 degrees.

A straight angle is a 180-degree angle, while acute angles are less than 90 degrees, obtuse angles are between 90 and 180 degrees, and reflex angles are greater than 180 degrees.

When two angles add up to 90 degrees, they are considered complementary angles, which means they complement each other to form a right angle.

When the sum of the measures of two angles is 180 degrees, they are known as supplementary angles as they add up to form a straight line.

In geometry, when a third line intersects two parallel lines, the third line is called a transversal. Transversals create special angle relationships such as corresponding angles, alternate interior angles, and alternate exterior angles.

Interior angles are the angles between two parallel lines that are on the same side of the transversal cutting across the lines.

When two parallel lines are intersected by a transversal line, the angles formed outside the parallel lines are called exterior angles. Interior angles are formed inside the parallel lines, adjacent angles share a common side and vertex, and alternate angles are a pair of non-adjacent angles formed by a transversal line.

Corresponding angles are angles that are on the same side of the transversal and in corresponding positions.

Perpendicular lines are two lines that intersect at a 90-degree angle. Parallel lines never intersect, intersecting lines intersect at any angle other than 90 degrees, and skew lines are non-coplanar lines that do not intersect.

Parallel lines are lines that are in the same plane and do not intersect at any point. Perpendicular lines intersect at a 90-degree angle, intersecting lines cross each other at points, and skew lines are non-coplanar lines that do not intersect and are not parallel.

Skew lines are lines that do not intersect and are not parallel. They lie in different planes and do not share a common point of intersection.

Vertical angles are the pairs of opposite angles formed by two intersecting lines. They are congruent angles and have equal measures.

A circle is defined as the set of all points in a plane that are equidistant from a given point, forming a closed curve. This geometric shape is different from a line, triangle, or square, which do not have all points equidistant from a single point.

The correct answer refers to the foundational point around which a circle is constructed.

An arc is a curved line that is part of the circumference of a circle. It is named by its endpoints. A chord is a straight line segment whose endpoints lie on the circle, a tangent is a line that touches the circle at exactly one point, and a secant is a line that intersects the circle at two points.

In geometry, a radius is a line segment with one endpoint at the center of a circle and the other endpoint on the circle itself. It is a crucial measurement in determining the size and properties of a circle.

A diameter is a line segment that passes through the center of a circle and whose endpoints lie on the circle, dividing it into two equal halves. A radius is a line segment that connects the center of a circle to any point on the circle. A chord is a line segment whose endpoints lie on the circle, but does not necessarily pass through the center. A tangent is a line that touches the circle at exactly one point, known as the point of tangency.

A chord is a line segment whose endpoints are any two points on a circle, whereas a diameter is a chord that passes through the center of the circle, a radius is a line segment from the center of the circle to any point on the circle, and a tangent is a line that intersects a circle at exactly one point.