place to stand

By William E. Steinman:

Geometry 2:

January 8, 2007:

A polygon is a closed plane figure bounded by straight line segments.

A triangle is a polygon with three sides.

Triangles can be classified in two ways.

They can be classified based on the equality of the lengths of their sides or based on the kind of angles they have.

We have three triangle forms based on equality of the length of their sides.

A scalene triangle is one having no congruent (equal length) sides.

For example, in a scalene triangle abc, a…b…c.

An isosceles triangle is one having at least two congruent sides.

The congruent sides are called the legs of the triangle. The remaining side is called the base of the triangle.

An equilateral triangle is one have three congruent sides. Thus, it is a special case of an isosceles triangle.

Triangles based of the kind of angles.

A right triangle is on which has a right (90^o) angle.

The perpendicular sides are called the legs of the right triangle.

The remaining side is called the hypotenuse of the right triangle.

This is a right triangle with sides abc. ab are the legs and c is the hypotenuse.

a c

We indicate the right triangle with the little square at the juncture of the legs.

An obtuse triangle is one having an obtuse angle. (More than 90^o and less than 180^o.) Her is an obtuse triangle.

An acute triangle is one having three acute angles. (Less than 90^o.)

Here is an acute triangle.

Lines in triangles:

An angle bisector of a triangle is a ray that bisects an angle and extends to the opposite side. The angle is divided into two equal angles.

A median of a triangle is a ray or line segment from a vertex to the midpoint of the opposite side.

A perpendicular bisector of a side of a triangle is a line that bisects and is perpendicular to the side.

Angle bisector: Median:

Perpendicular bisector:

An altitude of a triangle is a line segment from the vertex, which is perpendicular to the opposite side.

Hence, in an obtuse triangle the altitude drawn to either side of the obtuse angle will fall outside the triangle.

Happy days!