What Is the Linear Pair Postulate?
According to the linear pair postulate, two angles that form a linear pair are supplementary. A linear pair is a set of adjacent angles that form a line with their unshared rays. When added together, these angles equal 180 degrees. This postulate is sometimes call the supplement postulate.
The Greek mathematician Euclid is recognized as the father of geometry because of the contributions he made to the field. His book, "Elements," details 465 theorems and proofs that created the foundation of geometry as it's studied today. There are five geometric postulates explained in the book.
The first postulate states that it’s possible to draw a straight line between any two points. The second states that one can extend a straight line continuously. Another postulate describes a circle. Another asserts that all right angles are congruent. The fifth postulate remains unproven despite several attempts over the years to prove it.
Postulates vs. Theorems
Postulates are statements that have not been proven but are assumed to be true. For example, mathematicians believe the statement "through any two points there is exactly one line" despite the fact that it is not proven. A theorem is a true statement that one can prove. It is possible to prove the statement "If two lines intersect, then they intersect in exactly one point." Both postulates and theorems can be used to prove statements related to geometry.
Proofs in Geometry
In geometry, a proof is an argument that confirms or disproves a statement. The proof traces the series of facts, deductions and logic that support the final conclusion. Postulates like the linear pair postulate can be used in geometric proofs and mentioned in the justification section of the proof.
When two lines, line segments or rays intersect, they create spaces called angles. Mathematicians measure angles in degrees, and this measurement defines the type of angle. A straight angle (also known as a straight line) measures 180 degrees, and a right angle measures 90 degrees.
Obtuse angles measure greater than 90 degrees. Acute angles are less than 90 degrees. There are also angles with a space greater than 180 degrees called reflex angles. An angle reaches full rotation at 360 degrees. Angles can also be described as positive or negative, depending on the direction of the angle.
Understanding lines is a vital skill in the study of geometry. A series of points that extend indefinitely form a line. Lines don’t have end points. They have arrows denoting their infinite nature. A line segment is part of a line. Line segments have end points, which are points along the line. Rays start at a single point and extend infinitely in a single direction.
Parallel lines and line segments run side by side in a plane and never intersect. Perpendicular lines intersect and form a 90-degree angle at the point where they meet. These intersecting lines are a linear pair since their angles equal 180 degrees when added together.