**triangles**.

A triangle is another polygon, a planar figure with three sides.

Three is the fewest sides that a polygon can have, because you can't make an enclosed shape with only one or two straight lines.

*Does that mean that triangles are simple? Is class over? Can we go home?*

Not yet. We get to learn plenty of new words today.

Triangles are categorized by the length of their sides:

triangles have three sides that are of equal lengths.**Equilateral**

triangles have two sides that are equal in length.**Iscoceles**triangles have three different-length sides.**Scalene**

- A
triangle has one angle that measures 90 degrees.**right** triangles do not have a right angle.**Oblique**triangles have all three angles measuring less than 90 degrees (each).*Acute*triangles have one angle that's greater than 90 degrees.**Obtuse**

*.*

**hypotenuse**Triangles can be

*if they have the same angles but are different sizes. Triangles may be called*

**similar***if they are identical in every way, including size.*

**congruent**There are plenty of other characteristics of triangles. We don't have time to mention them all. This graphic shows some of them.

The

**orange**lines go from a vertex to the center of the opposite side.

The

**blue**lines originate from a vertex and intersect the opposite side at a right angle. This is called the

**altitude**. The point where the altitudes cross is the

**orthocenter**.

The

**green**lines are drawn midway along each side and intersect the sides at right angles. They cross at a single point within the triangle. These are the

**perpendicular bisectors**(mentioned yesterday).

The

**red**shows that a straight line can be drawn to connect the intersections of the

**orange**,

**blue**and

**green**lines. This is called Euler's Line, after the mathematician.

If you draw a few circles to help describe triangles, you will find that the center of the

**incircle**is where the triangle's

**angle bisectors**meet. That point is called the

**incenter**.

The

**circumcenter**is the center of the

**circumcircle**. It intersects the three verticles of the triangle. The circumcenter happens to land on the point where the three angle bisectors meet.

I'm stopping here because I am getting totally confused. We'll skip over calculating the area, sines and cosines, vectors, trigonometry and other aspects of triangles.

Some day we will tackle non-planar triangles - what happens when you draw a triangle over a curved surface, like the Earth - a global triangle.

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