Author Archives: hangtime

Parallel Lines & Transversals Problems

This video covers all those types of non-proof problem where they give you a couple or three parallel lines, with one or two transversals crossing them, and then you're supposed to solve for all the angles and x's all over the problem. They never end!

This video appears on the page: Parallel Lines & Transversals

Parallel Lines & Transversals Theorems

This video reviews the definitions and theorems that you'll need to know in order to do problems and proofs about parallels and transversals: alternating interior angles, alternating exterior angles, and corresponding angles.

This video appears on the page: Parallel Lines & Transversals

Parallel Lines & Transversals:
Parallel Lines & Transversals Theorems: Alternating Interior Angles, Alternating Exterior Angles, and Corresponding Angles
altParallel Lines & Transversals Problems

This section covers all those problems where a couple of parallel lines are crossed by another line (the transversal) and you're then supposed to figure out all the angles, and show which ones are congruent.

Part of the course(s): Geometry

Secant Length Problems (in Circles)

This video focuses on how to find the length of secants and secant segments using the ab=bc formula, sometimes written as a(a+b)=c(c+d). This video also covers the most common type of error students make on these, namely not making sure that you're plugging the right length into the formula.

This video appears on the page: Formulas for Secants & Chords

Secant Angle Problems (for Circles)

This video focuses on the problems where you have two secants and the intercepted arcs between them. You then use the "half the difference" formula to find the missing angle or arc.

This video appears on the page: Formulas for Secants & Chords

Formulas for Lengths & Angles of Chords & Secants

This video is a quick review of the formulas for chords and secants. For lengths of chords and secants we've got ab=cd and a(a+b)=c(c+d). For angles between chords and secants, we've got the "half the sum" and "half the difference" formulas. This video focuses on how to remember all these, and how to keep chords and secants straight.

This video appears on the page: Formulas for Secants & Chords

Formulas for Secants & Chords
Formulas for Lengths & Angles of Chords & Secants
Segment Lengths of Intersecting Chords (ab=cd)
Chord Angles and Intercepted Arcs
Secant Angle Problems (for Circles)
Secant Length Problems (in Circles)

Videos covering problems where two secants meet outside a circle, and the problem asks you to calculate the length of the segments, or the angle between them.

Part of the course(s): Geometry

Circles in X-Y Coordinates

This video covers equations of circles in X-Y coordinates. This topic isn't covered by most geometry teachers, but if it's in your class, here you go. For equations of other conics, like ellipses and parabolas, check out the Algebra 2 page.

Part of the course(s): Geometry

Tangent Proofs

First off we'll review the theorems for tangents, then we'll prove the one about how tangents from a single point are congruent. Hint: congruent triangles are involved.

This video appears on the page: Tangents of Circles

Tangents & Inscribed Angles

This is a short video, but it's an important one that addresses the hardest-to-spot tangent problems: the ones where they give you the length of an arc. If you're not on the lookout, you won't realize that arc is inscribed by an angle where one side is a tangent to the circle!

This video appears on the page: Tangents of Circles

Circle Tangent Problems

This is a long video because there's a lot of ground to cover! I work all the most common types of questions, involving both the fact that tangents are perpendicular to the radius they intersect as well as problems where you have to solve for the length of tangents.

This video appears on the page: Tangents of Circles

Tangent Theorems

This video is a quick summary of the theorems you should know for tangents to circles, whether you're working problems or looking for hints for your next proof.

This video appears on the page: Tangents of Circles

Internal vs External Common Tangents

This video covers the situation where you have two circles and you're supposed to classify them. If the circles themselves are tangent, they can be "internally" or "externally" tangent. More common is that a segment is tangent to both circles, and you're supposed to know if that "common tangent" is internal or external.

This video appears on the page: Tangents of Circles

Tangents of Circles:
Internal vs External Common Tangents
Tangent Theorems
Circle Tangent Problems
Tangents & Inscribed Angles
Tangent Proofs

Not to be confused with trig tangents, circle tangents are segments which sidle up alongside a circle and intersect it at exactly one point. This chapter covers the definition, problems and theorems, including how inscribed angle theorems apply to tangents.

Part of the course(s): Geometry

Circle Chord Proofs

In previous videos we saw all the different chord theorems. Now it's time to put a few of them into practice in proofs! We'll even prove a couple of chord theorems, which is a popular homework question.

This video appears on the page: Chords

Chord Angles and Intercepted Arcs

At this point in the circles chapter, you already know what to do when a missing angle is at the center of a circle (central angle) or on the edge (inscribed angles). But what if it's an angle between two chords that's not on the edge or in the middle? Well, it's "half the sum" of the two intercepted arcs, of course!

This video appears on the page: Chords ,Formulas for Secants & Chords

Segment Lengths of Intersecting Chords (ab=cd)

These problems are the ones where you have two chords intersecting, and if you multiply the two halves of one chord you'll get the same product as when you multiply the halves of the other chord. Depending on how you label things: ab=cd or ad=bc, or ac=db.

This video appears on the page: Chords ,Formulas for Secants & Chords

Equidistant Congruent Chords

Examples involving two theorems: One theorem says chords equidistant from the center of a circle are congruent. The other theorem says that if a chord hits a diameter at a right angle it bisects the chord, and vice versa. The takeaway: If you see a "T" shape inside a circle, you've probably got a right angle and some congruence.

This video appears on the page: Chords

Chord Problems Involving Triangles

There are so many types of chord problems, but this video covers just the type where chords form triangles inside of circles: inscribed triangles, inscribed triangles in semicircles, triangles formed by intersecting chords... If there's a triangle somewhere in a circle, this video is a good place to start.

This video appears on the page: Chords

Chord Problems with Congruent Arcs

This video covers one of the many types of chord problems: the type using the theorem that congruent arcs have congruent chords, and vice versa. Also covered are more complicated problems where the congruent arcs theorem is mixed in with older material, like central and inscribed angles.

This video appears on the page: Chords