Khan Academy on a Stick
Special properties and parts of triangles
You probably like triangles. You think they are useful. They show up a lot. What you'll see in this topic is that they are far more magical and mystical than you ever imagined!

Circumcenter of a Triangle
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Multiple proofs showing that a point is on a perpendicular bisector of a segment if and only if it is equidistant from the endpoints. Using this to establish the circumcenter, circumradius, and circumcircle for a triangle

Circumcenter of a Right Triangle
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Showing that the midpoint of the hypotenuse is the circumcenter

Three Points Defining a Circle
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Three points uniquely define a circle. The center of a circle is the circumcenter of any triangle the circle is circumscribed about.

Area Circumradius Formula Proof
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Proof of the formula relating the area of a triangle to its circumradius

2003 AIME II Problem 7
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Area of rhombus from circumradii of triangles
Perpendicular bisectors
In this tutorial, we study lines that are perpendicular to the sides of a triangle and divide them in two (perpendicular bisectors). As we'll prove, they intersect at a unique point called the cicumcenter (which, quite amazingly, is equidistant to the vertices). We can then create a circle (circumcircle) centered at this point that goes through all the vertices. This tutorial is the extension of the core narrative of the Geometry "course". After this, you might want to look at the tutorial on angle bisectors.

Point Line Distance and Angle Bisectors
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Thinking about the distance between a point and a line. Proof that a point on an angle bisector is equidistant to the sides of the angle and a point equidistant to the sides is on an angle bisector

Incenter and incircles of a triangle
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Using angle bisectors to find the incenter and incircle of a triangle

Inradius Perimeter and Area
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Showing that area is equal to inradius times semiperimeter

Angle Bisector Theorem Proof
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What the angle bisector theorem is and its proof

Angle Bisector Theorem Examples
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Using the angle bisector theorem to solve for sides of a triangle
Angle bisectors
This tutorial experiments with lines that divide the angles of a triangle in two (angle bisectors). As we'll prove, all three angle bisectors actually intersect at one point called the incenter (amazing!). We'll also prove that this incenter is equidistant from the sides of the triangle (even more amazing!). This allows us to create a circle centered at the incenter that is tangent to the sides of the triangle (not surprisingly called the "incircle").

Triangle Medians and Centroids
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Seeing that the centroid is 2/3 of the way along every median

Triangle Medians and Centroids (2D Proof)
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Showing that the centroid is 2/3 of the way along a median

Medians divide into smaller triangles of equal area
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Showing that the three medians of a triangle divide it into six smaller triangles of equal area. Brief discussion of the centroid as well

Exploring Medial Triangles
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What a medial triangle is and its properties

Proving that the Centroid is 23rds along the Median
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Showing that the centroid divides each median into segments with a 2:1 ratio (or that the centroid is 2/3 along the median)

Median Centroid Right Triangle Example
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Example involving properties of medians
Medians and centroids
You've explored perpendicular bisectors and angle bisectors, but you're craving to study lines that intersect the vertices of a a triangle AND bisect the opposite sides. Well, you're luck because that (medians) is what we are going to study in this tutorial. We'll prove here that the medians intersect at a unique point (amazing!) called the centroid and divide the triangle into six mini triangles of equal area (even more amazing!). The centroid also always happens to divide all the medians in segments with lengths at a 1:2 ration (stupendous!).

Proof  Triangle Altitudes are Concurrent (Orthocenter)
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Showing that any triangle can be the medial triangle for some larger triangle. Using this to show that the altitudes of a triangle are concurrent (at the orthocenter).

Common Orthocenter and Centroid
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Showing that a triangle with the same point as the orthocenter and centroid is equilateral
Altitudes
Ok. You knew triangles where cool, but you never imagined they were this cool! Well, this tutorial will take things even further. After perpendicular bisectors, angle bisector and medians, the only other thing (that I can think of) is a line that intersects a vertex and the opposite side (called an altitude). As we'll see, these are just as cool as the rest and, as you may have guessed, intersect at a unique point called the orthocenter (unbelievable!).

Review of Triangle Properties
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Comparing perpendicular bisectors to angle bisectors to medians to altitudes

Euler Line
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The magic and mystery of the Euler Line

Euler's Line Proof
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Proving the somewhat mystical result that the circumcenter, centroid and orthocenter
Bringing it all together
This tutorial brings together all of the major ideas in this topic. First, it starts off with a lightweight review of the various ideas in the topic. It then goes into a heavyweight proof of a truly, truly, truly amazing idea. It was amazing enough that orthocenters, circumcenters, and centroids exist , but we'll see in the videos on Euler lines that they sit on the same line themselves (incenters must be feeling lonely)!!!!!!!