TRIANGLES

A triangle is a plane shape having 3 sides. Its name is derived from its three (tri) angles.

Other facts help define a triangle.

1. The sum of the angles in any triangle equals 180.

2. A triangle is the only plane shape which maybe defined in terms of its sides only; in all others one or more angles must be stated.

Types of Triangles

There are four kinds of triangles. They are classified according to the size of their sides and angles as follows:

1. Equilateral-all sides are equal-all angles are equal-all angles are 60

2. Isosceles-two sides equal-two angles equal

3. Scalene-all sides unequal-all angles unequal 4. Right-one right angle

Altitudes and Medians

The altitude and median of a triangle are not the same; the difference is pointed out in the following definitions:

1. The altitude of a triangle is a line drawn from the vertex, perpendicular to the base.

2. The median of a triangle is a line drawn from the vertex to the midpoint of the base.

Construction of Triangles

There are many ways to construct a triangle, depending upon what measurements are known to you. The following examples will assist you. Select the appropriate method according to the information given about the triangle.

1. A triangle may be constructed if the lengths of three sides are known.

Problem:

Construct a triangle. Given:

Three sides of a triangle: 2", 1", 1 1/2".

Solution:

Step 1. Draw a base line equal to one of the sides. Mark the ends of lines A and B.

Step 2. Set the compass equal to the second side (1" in the above) and swing an arc from A.

Step 3. Set the compass equal to the third side (1 1/2" in this case) and swing an arc.

Conclusion:

The intersection of these two arcs will be the vertex C and will complete triangle ABC.

2. A triangle maybe constructed if two sides and the included angle (angle between the sides) are known.

Problem:

To construct a triangle with two sides and the included angle known.

Given:

Two sides 1 1/2" and 2 1/4" and the included angle.

Solution:

Step 1. Draw the base equal to one side.

Step 2. Construct an angle equal to the given angle.

Step 3. Measure the second side on the side of the angle and connect the ends of the given sides BC.

Conclusion:

Triangle ABC has been constructed with two sides and the included angle given.

3. A triangle maybe constructed if two angles and the included side are given.

Problem:

Construct a triangle.

Conclusion:

Triangle ABC has been constructed with two angles and the included side given.

4. A right triangle may be constructed if the two sides adjacent to the right angle are known.

Problem:

Construct a right mangle whose sides adjacent to the right angle are 1 1/2" and 1".

Solution:

Step 1. Draw AB 1 1/2" long.

Step 2. At A, erect a perpendicular to AB.

Step 3. Locate point C 1" from AB and complete the triangle.

Conclusion:

Triangle ABC is a right triangle,

5. A right triangle maybe constructed by making the sides 3", 4", and 5" or multiples or fractions thereof.

Problem:

Construct a right triangle with sides of 1 1/2", 2", and 2 1/2" (1/2 of 3,4, and 5).

Solution:

Step 1. Draw line AB = 2".

Step 2. From A, draw an arc equal to 1 1/2".

Step 3. From B, draw an arc equal to 2 1/2".

Conclusion:

Triangle ABC is a right triangle,

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