Author Archives: hangtime
Segment Addition Postulate (AB+BC=AC)
This video covers the Segment Addition Postulate, which basically says that if you break a segment into two parts, the lengths of the two parts are going to add up to the length of the original segment. Shocking!
This video covers the Segment Addition Postulate, which basically says that if you break a segment into two parts, the lengths of the two parts are going to add up to the length of the original segment. Shocking!
The Ruler Postulate
This video covers the Ruler Postulate, which is basically "geometry speak" for finding the distance between two points on the number line by subtracting their coordinates. Good stuff!
This video covers the Ruler Postulate, which is basically "geometry speak" for finding the distance between two points on the number line by subtracting their coordinates. Good stuff!
By request, this chapter video covers the most important skill you'll need for Algebra and beyond: addition and subtraction of negative numbers using the number line. You can add and subtract any number with the number line, but negatives are where it's really great.
Adding & Subtracting Using The Number Line
This video covers the absolutely most important thing you can do with a number line: addition and subtraction, especially when negative numbers are involved. People who can do math in their heads are all using this technique. Visually. In their minds. 7.NS.1, 7.NS.2, 7.NS.3
Congruent Segments on the Number Line
This video covers the problems where you are given segments on a number line and you have to know if they're congruent or not.
The Number Line
This video introduces the number line, and it explains what you need to know about those number line definitions in books that always begin with crazy phrases like "There exists a line with a correspondence between real numbers and..." Yikes!
This video introduces the number line and explains how to use it to add and subtract negative numbers. It also explains how to determine if segments on the number line are congruent.
Definition of Midpoint
This video explains what the midpoint is, how to solve for x in midpoint problems, and the most important way that midpoint will be used in geometry proofs.
Videos covering the definition of midpoint, as well as how to find the coordinates of the midpoint of a line segment in the X-Y plane.
Parallel Lines & Proportional Transversals
This video covers the problems where you have three parallel lines that are cut by more than one transversal, and the theorem that says the transversals will be cut into proportional segments by the parallel lines.
Right Triangle Similarity Theorems: "Geometric Mean"
There are three theorems about right triangles which have been cut in half with the "altitude to the hypotenuse". These geometric mean theorems are super-confusing, so I explain how to make sense of it by always setting up a proportion so you don't have to memorize the crazy equations.
Similar Triangle Proofs
In this video I do a few proofs using the AA Postulate, and the SAS Similarity Theorem. And I explain what to look for in these types of proofs, where the given info sometimes includes random equations like AB x BD = CB x AD.
Using SSS & SAS Similarity Theorems
This video goes through a bunch of the most common similar triangles problems you'll see, including the ones where you have to say if two triangles are similar or not and why. It also shows a couple of common diagrams for proportional triangles that you should know.
Similar Triangle Theorems & Postulates
This video first introduces the AA Triangle Similarity Postulate and the SSS & SAS Similarity Theorems. Then it gets into the triangle proportionality theorem, which also says that parallel lines cut transversals proportionately they cut triangles.
If you need to find missing sides of similar triangles, that is mostly covered in the similar polygons chapter videos. Instead, this chapter of videos on similar triangles focuses on similarity theorems and proofs for triangles. Also covered are right triangle problems involving the "geometric mean" of various sides and the "altitude to the hypotenuse" of right triangles.
The videos in this chapter explain what similar triangles and similar polygons are, and how to solve various types of problems including: scale factors, missing sides, similar trapezoids. Also explained are which types of polygons are always similar (i.e. squares, equilateral triangles, special right triangles, etc).
Scale Factors Between Similar Triangles & Polygons
A scale factor just tells you how much bigger one shape is that another that it's similar to. If something is twice as big, the scale factor is 2. Three times the size, the factor is 3. This video explains how to find the scale factor, and then how to use it once you have it.