Now let us move onto geometry theorems which apply on triangles. If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary.Īngles that are opposite to each other and are formed by two intersecting lines are congruent. If two angles are both supplement and congruent then they are right angles. If two angles are supplements to the same angle or of congruent angles, then the two angles are congruent. If two angles are complementary to the same angle or of congruent angles, then the two angles are congruent. One way to find the alternate interior angles is to draw a zig-zag line on the diagram. The alternate interior angles have the same degree measures because the lines are parallel to each other. When two parallel lines are cut by a transversal then resulting alternate interior angles are congruent. The alternate exterior angles have the same degree measures because the lines are parallel to each other. When two parallel lines are cut by a transversal then resulting alternate exterior angles are congruent. Some of the important angle theorems involved in angles are as follows: 1. The relation between the angles that are formed by two lines is illustrated by the geometry theorems called “Angle theorems”. To make it easier to connect and hence apply, we have categorized them according to the shape the geometry theorems apply to. Now that we are familiar with these basic terms, we can move onto the various geometry theorems. If there are two lines crossing from one particular point then the opposite angles made in such a condition are equals. When the perpendicular distance between the two lines is the same then we say the lines are parallel to each other. Then the angles made by such rays are called linear pairs. When two or more than two rays emerge from a single point. Two rays emerging from a single point makes an angle. Now let’s discuss the Pair of lines and what figures can we get in different conditions. Line SegmentĪ line having two endpoints is called a line segment. LineĪ straight figure that can be extended infinitely in both the directions RayĪ line having one endpoint but can be extended infinitely in other directions. In maths, the smallest figure which can be drawn having no area is called a point. Let us go through all of them to fully understand the geometry theorems list. Key components in Geometry theorems are Point, Line, Ray, and Line Segment. To prove a Geometry Theorem we may use Definitions, Postulates, and even other Geometry theorems.įor example: If I say two lines intersect to form a 90° angle, then all four angles in the intersection are 90° each. Unlike Postulates, Geometry Theorems must be proven. We can also say Postulate is a common-sense answer to a simple question. Or when 2 lines intersect a point is formed. It is the postulate as it the only way it can happen.
It’s like set in stone.Įxample: - For 2 points only 1 line may exist. Geometry Postulates are something that can not be argued.
This is what is called an explanation of Geometry. Or did you know that an angle is framed by two non-parallel rays that meet at a point? So before moving onto the geometry theorems list, let us discuss these to aid in geometry postulates and theorems list.ĭefinitions are what we use for explaining things.Į.g.: - You know that a circle is a round figure but did you know that a circle is defined as lines whose points are all equidistant from one point at the center. The guiding light for solving Geometric problems is Definitions, Geometry Postulates, and Geometry Theorems. Geometry is a very organized and logical subject.
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