Alternate Interior Angles Theorem: If two parallel lines are intersected by a transversal, then alternate interior angles are equal in measure.Corresponding angles postulate: If two parallel lines are intersected by a transversal, then the corresponding angles have equal measure.a straight angle), then the angles are supplementary angles.

Linear Pair Theorem: If two angles form a linear pair (ie.The following are examples of angle theorems and postulates: For example, angles of elevation and depression word problems require the use of the alternate interior angles theorem. There are also many angle theorems and postulates that are useful in studies of geometry and trigonometry. The postulate tells us that the only way L1 and L2 will intersect is on the side where the angles are each less than 90 degrees. Angles A and B are each less than 90 degrees. There is a third line that intersects both of these lines. In the diagram, we have two lines: L1 and L2. Pretty confusing, right? To help you understand Euclid’s fifth postulate, I have included an important diagram below. Euclid’s Fifth Postulate: If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.A circle may be drawn with a center and any radius.Įuclid’s fifth postulate, however, is know for its length, wordiness, and confusing nature:.A line segment may be extended indefinitely.A straight line may be drawn between any two points.The first four postulates are quite simple without the need for much mathematical reasoning: Euclid has five famous postulates that are some of the most important in the study of geometry. I have included a few examples and diagrams because I think this is an important part of learning geometry! Many times, these postulates sound so confusing that you need a diagram! Euclid’s 5 PostulatesĮuclid was a Greek mathematician who’s postulates and axioms form the basis of much of the geometry that we study today.

Now that you understand the difference between geometry theorems and postulates, you are ready to dig into this geometry theorems and postulates list with examples. Geometry Theorems and Postulates List with Examples And there isn’t a geometry proof that can show this postulate to be false (unless you are in non-Euclidean space, but that is a topic for another day!).

It is hard to argue this postulate, isn’t it? You can’t make the line pass through the point in a different way that is still parallel to the other line. For example, the parallel postulate tells us that for a given point not on a line, there is only one line passing through that point that is parallel to the other line. In most cases, postulates don’t actually need a proof.

Notice the difference between theorems and postulates here! So if geometry theorems are proven using postulates, what are geometry postulates? We can define postulates as statements that we assume are true without proving them. There are many examples of common geometry theorems that you have likely explored already! For example, the angle sum theorem tells us that the sum of the measures of the angles in a triangle will add up to 180 degrees. In Euclidean geometry, we use a mathematical system that relies on theorems to help us solve a variety of different geometric problems. Simply put, we can prove geometry theorems by using other known geometry facts. In the study of geometry in general, a theorem is a statement that can be proven by using definitions, postulates, or other proven theorems. That’s why I’ve put together this handy geometry theorems and postulates list with examples to help you dig into the most important ones! What are Geometry Theorems? Many geometric problems require a strong knowledge of geometry theorems and postulates.

Geometry theorems list