Geometry

A statement is a sentence that has only one truth value. When you negate a statement, the opposite truth value is assigned.

Compound statements are formed by “and” or “or”. one is a conjunction while the other is a disjunction. Find out more info in the lesson!

A conditional statement or “if-then” statement is useful for logic and reasoning. Truth tables are critical for understanding the truth values!

What is a biconditional statement? What is “if and only if” or “iff”? Find out here in this lesson video!

Learn the basics of reasoning and how to simply disprove a statement through the use of counterexamples. Discussed terms include conjecture, inductive reasoning, and more!

In this lesson video, I explain two different laws that are handy for proving through reasoning! Stay tuned!

A plane is made up of lines which are made up of points. Find out how it all relates in this lesson video!

What is a postulate? Find out in this video where I also explain 3 different postulates: two-point, line-point, and line intersection postulate.

Let’s move on to discussing Three-Point Postulate, Plane-Point Postulate, Plane-Line Postulate and Plane Intersection Postulate. All of which are helpful for understanding planes!

A ray is simply a line with one endpoint where a segment has 2 endpoints. See them drawn out and explained in this lesson video!

One is a standard unit of measure whereas the other is a metric way of measuring. Which one is related to feet? And which is related to meters?

Congruent segments are 2 different segments with the same length. Their orientation may be different, but their lengths must be the same!

What exactly does it mean when we say that a point is “between” two other points? Learn about the formal definition of “betweeness” in this video!

A proof explains why a conjecture is true for a given situations. Here we will start bringing together our logic and reasoning to explain geometric theorems!

Let’s go over a few different properties in order to utilize them in a simple 2-colum proof. A 2-column proof is a great way to organize your logic!

In this lesson, we will prove our first theorem, the Segment Congruence Theorem. I will show you the form in both paragraph and 2-column.

An angle is formed by two rays extending from the same endpoint. And how do we measure that angle? In degrees! Find out more in this lesson video.

Now that we know what is used to measure an angle, how exactly to we calculate that measurement? One way is with a protractor! In this video, I will show you how to use an read this helpful tool.

Here we will go over two postulates: the ruler postulate and the protractor postulate. Fill in the blanks on the worksheet and keep it in your notebook for future reference!

In this lesson video, we will discuss the three different categories of angle: right, obtuse, and acute. Come up with some handy sayings on your own to help remember which is 90 degrees, which is greater than 90, and which is smaller.

Congruent angles are angles that have the same measure which we can also say the same degrees. An angle bisector splits or divides one angle into multiple angles. Do you think an angle bisector can form two congruent angles?

The angle congruence theorem simply states that if one angle is congruent or the same size as another angle. Well, then that new angle is the same size as the original.

In this lesson video, we will learn about complementary and supplementary angles. After watching, wee if you remember which adds up to 90 degrees and which adds up to 180 degrees!

There are new two theorems we will go over in this lesson. One is the congruent supplements theorem and the other is the congruent complements theorem.

In this video, we will learn new terms for angles such as vertical, adjacent, and linear pair. Each definition will be useful when calculating angle measures and then proving that measure in later videos. So stay tuned!

The angle addition postulate sets up a foundation for understanding the addition of angle measures. In this video, we also go over the linear pair theorem!

Walk through the proof of the vertical angle theorem to help better understand how and why this theorem holds true.

You may have been introduced to parallel and perpendicular lines previously in regards to our Algebra classes. Now we will discuss the geometry aspect which will help us in proofs later on!

Transversals are lines that intersect or cross at least two lines in a plane at separate points. See how the linear pair theorem may be used here!

In this video, we begin tying together many different vocabulary words, definitions, and postulates to help form a new theorem: the Alternate Interior Angle Theorem.

We will continue on like the last video now branching on to Consecutive Interior and Alternate Exterior Theorem. Compare all of our new angle theorems to help get a better understanding!

Continuing on, in this lesson video, we will learn yet another new theorem regarding angles: the Converse Angle Theorem.

In the last video of this chapter, we will learn all about the perpendicular transversal theorem and how to prove it!

In this lesson video, I will introduce many different polygons with various numbers of sides. Starting with triangle and working our way up to an n-gon!

The last video was a quick introduction to the basic polygons. In this lesson video, we will discuss polygons in more detail such as convex vs concave and regular polygons!

The perimeter is the total length of all the sides on a figure. Let’s go over how to calculate and measure in this video.

We can use the Pythagorean Theorem to help us calculate distance. Remember this key concept because it will come up again in Algebra and Calculus!

Now that we understand distance, we can learn how to calculate the midpoint! Find out how in this lesson video.

We will learn a new theorem: the Midpoint Theorem. As well as how to calculate the distance between a point and a line.

In this lesson video, I discuss edges and vertices as well as different measures of polygon angles. Stay tuned!

This chapter is all about TRIANGLES! Learn how to classify based on sides and angles in this video.

The three different angles within a triangles add up to equal 180 degrees. But why? And how? Find out in this lesson video!

The Third Angle Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent. Prove it!

Triangle exterior angles are formed by one side of the triangle and the extension of the connecting side. This lesson video also teaches about the Triangle Exterior Angle Theorem.

So far we have done over definitions, postulates, and theorems. In this lesson, we will discuss a corollary and introduce the first one we will use in our Geometry series.

CPCTC, what does it stand for? Learn all about the definition of congruent triangles and the Triangle Congruence Theorem.

The Side-Side-Side Postulate or SSS for short is one of the simplest ways to tell if two triangles are congruent. See how to use it here.

Now that we’ve learned all about thee SSS Postulate, we can move on to the SAS postulate also called the Side-Angle-Side.

We will learn two more postulate in this video, Angle-Side-Angle and Angle-Angle-Side (ASA and AAS) to go along with the previous two SSS and SAS.

Let’s bring back that right triangle and learn how to use it in order to prove if two triangles are congruent. Stay tuned for more right angle tips!

For proving the Isosceles Triangle Theorem, we will bring together our knowledge of triangles and logic in a paragraph form. We will also learn the converse and two other corollaries.

Join me as I discuss the perpendicular bisector, its theorem, and its converse. In this lesson video, I also introduce the definition of concurrent lines and the circumcenter theorem.

Discover angle bisectors and their theorem and also the converse of the angle bisector theorem in this detailed lesson video.

Along with the centroid we can define other inside parts of a triangle such as the median and altitude of the figure.

We have previously learned about inequalities within our Algebra classes. We will now learn about them as they relate to Geometry and introduce a new theorem or two using them.

We have written proofs in both a list and paragraph form using a given method to work through our logic. In this lesson, we will learn a new way to prove a statement using an indirect proof.

In this 10 minute video, I will walk you through how to prove the Long Side, Large Angle Theorem and discuss the Large Angle, Long Side Theorem.

The paragraph proof may be a bit wordy, but stick with me as I help you prove the Triangle Inequality Theorem in paragraph proof form.

In this lesson video, I will go through the steps of how to prove yet another theorem: the SAS Inequality – Hinge Theorem. And remember, once a theorem is proved, you may use it to prove other theorems!

Lastly in this chapter of the video series, we will prove the SSS or Side-Side-Side Inequality Theorem. Great job thus far!

We have discussed at length on the idea of congruence and in this video I will introduce similarity, another key concept in Geometry.

Let’s go over three new theorem relating to sides and angles of triangles except now we will use them for similarity.

Learn all about reflexive, symmetric, and transitive similarities within triangles and their theorem.

In many Algebra classes we introduce similarity and proportions together because each can be used to describe the other. This is the same in Geometry as well!

We know about a midpoint, but what is a midsegment and how do we prove the given theorem. Learn all about it once you click play!