Author Archives: hangtime

Triangle Inequality Theorems--SSS, SAS Between Triangles

This video covers the theorems that compare triangle side lengths between two different triangles. Geometry being designed to make things confusing for you, naturally these two theorems have the exact same name as congruency theorems you already know: SAS and SSS. Ain't geometry great!

This video appears on the page: Triangle Inequalities & Side Lengths

Triangle Inequality Theorems--Within Single Triangle

This video covers how to put the angles in a triangle in order from biggest to smallest, within a single triangle. a

This video appears on the page: Triangle Inequalities & Side Lengths

Triangle Inequalities & Side Lengths:
Triangle Inequality Theorems--Within Single Triangle
Triangle Inequality Theorems--SSS, SAS Between Triangles
Distance from Points to Lines & Planes

These videos cover a few theorems that all involve "inequalities". In previous chapters, you were always trying to prove two triangles or segments congruent. In this one, you're trying to prove things unequal, whether it's saying that one side in a particular triangle is longer than another side, or that a side in one triangle is longer than a side in another.

Part of the course(s): Geometry

Indirect Proofs

These are pretty confusing for everyone when you first see them, but then at some point you hopefully are given step-by-step instructions to make these easy. This is that moment for you!

Part of the course(s): Indirect Proofs ,Geometry

Indirect Proofs

These are pretty confusing for everyone when you first see them, but then at some point you hopefully are given step-by-step instructions to make these easy. This is that moment for you!

This video appears on the page: Indirect Proofs

Angle and Segment Bisectors
Segment Perpendicular Bisectors
Angle Bisectors in Triangles

These videos cover a couple of theorems about the bisectors of angles and segments. I'll save you the suspense: both involve things being equidistant, and result in congruent triangles.

Part of the course(s): Geometry

Angle Bisectors in Triangles

This video covers the theorem that states that if a point is on an angle's bisector, it's equidistant from the sides of the angle. Not surprisingly, this will create congruent triangles! Geometry is so predictable...

This video appears on the page: Angle and Segment Bisectors

Segment Perpendicular Bisectors

This video covers one type of bisector, the type that splits a segment into two congruent halves at a right angle. The theorem states that if a point is on a segment's perpendicular bisector, it's equidistant from the segment's endpoints, resulting in... congruent triangles!

This video appears on the page: Angle and Segment Bisectors

Medians, Midsegments, Altitudes & Centroids (of Triangles)
Midsegments of Triangles
Medians, Centroids & Orthocenters

The videos in this section cover a few different random topics in triangles that didn't really fit in anywhere else.

Part of the course(s): Geometry

Medians, Centroids & Orthocenters

This video covers a grab bag of fun geometry terms, including the circumcenter. Most of this stuff you'll never see again, but it's kind of cool that the centroid of a triangle is also it's center of gravity, or balance point.

This video appears on the page: Medians, Midsegments, Altitudes & Centroids

Midsegments of Triangles

This is that thing where a segment is drawn across a triangle, parallel to one side while hitting the other two sides in their midpoints.

This video appears on the page: Medians, Midsegments, Altitudes & Centroids

Isosceles Triangle Theorem Proofs

Full proofs for the Isosceles Triangle Theorem, its converse the Base Angle Theorem, and the corollaries.

This video appears on the page: Isosceles & Equilateral Triangle Theorems

Isosceles & Equilateral Triangle Problems

This video covers how to do non-proof problems involving the Isosceles Triangle Theorem, its converse and corollaries, as well as the rules around equilateral and equiangular triangles.

This video appears on the page: Isosceles & Equilateral Triangle Theorems

Isosceles Theorem, Converse & Corollaries

This video introduces the theorems and their corollaries so that you'll be able to review them quickly before we get more into the gristle of them in the next couple videos. Also known as the Base Angle Theorem, in total these theorems also cover equilateral and equiangular triangles.

This video appears on the page: Isosceles & Equilateral Triangle Theorems

Isosceles & Equilateral Triangle Theorems:
Base Angle Theorem
Converse
& Equilateral Corollaries

Between the main theorem and the corollaries, you wouldn't believe how often you're going to come across this theorem throughout your academic career, from trig to physics to calculus to architecture and design. And the SAT!

Part of the course(s): Geometry

HL, HA, LL, LA Proof Examples

Full proofs using these most special of right-angle theorems. Don't watch these if your class doesn't cover them, though, because you won't be allowed to use them on tests.

This video appears on the page: Right Triangle Congruence

HL, HA, LL, LA Theorems

With the exception of H-L, most of these aren't covered by most teachers because they're not really necessary. If your class does use them, though, this video will explain what they are and how they're derived from SAS, ASA, and AAS.

This video appears on the page: Right Triangle Congruence

Right Triangle Congruence:
H-L, L-L
H-A, L-A

Many geometry teachers don't cover all of these because they're redundant, right-triangle-only versions of all the congruence theorems you already know. The only one that every teacher covers is H-L.

Part of the course(s): Geometry

CPCTC Proof Examples

Get ready for some major proof action as we learn how to use CPCTC as an additional step after more typical SSS, SAS, ASA, and H-L proofs.

This video appears on the page: CPCTC

CPCTC Theorem

Corresponding Parts of Congruent Triangles are Congruent. Just five little words, yet they cause so much trouble and so many proofs! Well, get ready for the awesome as we apply this gem to SSS, SAS, ASA, AAS, and H-L.

This video appears on the page: CPCTC