Triangles

Examples of Triangles

A triangle is a special kind of shape.




What do you think makes a shape a triangle?
Be sure to think about this question before going on with the lesson


Properties of triangles
Before we decide exactly what makes a shape a triangle, we need to understand what a closed figure is.
A figure is closed if all its sides are connected.

These figures are closed.	These figures are not closed.

A triangle is a closed figure with three sides.

Use this definiton to figure out which of the following shapes are triangles and which are not.






Classification of Triangles
There are many different kinds of triangles.
The following table outlines some basic types of triangles.

	Acute trianlges are triangles in which the measures of all three angles are less than 90 degrees.
	Obtuse triangles are triangles in which the measure of one angle is greater than 90 degrees.
	Right triangles are triangles in which the measure of one angle equals 90 degrees.
	Equilateral triangles are triangles in which all three sides are the same length.
	Isosceles triangles are triangles in which two of the sides are the same length.
	Scalene triangles are triangles in which none of the sides are the same length.

Triangular Grid Activity
The following grid was formed by three sets of parallel lines.

You can print out the grid and complete the following activity:

• Outline one of the inner triangles on the above grid and label the angles A, B, and C.
• Choose three different color crayons, pencils, or markers.
• With the first color, color in angle A and all angles in the grid congruent to angle A.
• With the second color, color in angle B and all angles in the grid congruent to angle B.
• With the third color, color in angle C and all angles in the grid congruent to angle C.

Study the result and answer the following questions:
1) What do you observe about the angles around A, B, and C?
2) Find a straight angle. What color are the angles that make up the straight angle? Repeat this procedure for three other straight angles in the grid.
3) What colors are the angles of triangle ABC?
4) What conjecture can you make about the sum of the angles of triangle ABC?
5) Do you think this conjecture is true for all triangles? Why or why not?



The Geometer's Sketchpad Activity
Explore the angles of a triangle using the Geometer's Sketchpad by clicking on the picture below.


Did the conjecture you made in the triangular grid activity also hold in the Geometer's Sketchpad activity?