Notes for Homework #2

Notes for defining triangles by angles in degrees 

Notes for defining triangles by three points in the plane, finding the area and the classifications by finding the distances
 

Notes for Homework #1

Notes for defining triangles by side lengths.

Notes for degenerate triangles.

Notes for Heron's formula.
 

Degenerate triangles

The triangle inequality state that if the sides of a triangle are labeled a, b and c, we need two inequalities to be true a + b >= c >= |a - b|. If we get an equality, the triangle is said to be degenerate. For example, if the lengths are 9, 6 and 3, we would draw a line segment of length 9 with a point on the line splitting into two parts of length 6 and 3. To think of it in terms of base and height, the base would be 9 and the height 0, so the area would be zero.

There are some facts about degenerate triangles you should know.

a) If you plug in these values into Heron's formula, you will get an area of 0.

b) The angle sum is 180°, since there are angles of 180°, 0° and 0°. It is not truly obtuse, since 180° is a straight angle.

c) If the two short sides are equal, it qualifies as an isosceles triangle, if they are not equal, it is scalene.

d) When we define a triangle by three distinct points in the plane, we will get a degenerate triangle if the three points are all on the same line, which is known as colinear.