TRIANGLE IN PLANE GEOMETRY

 
A triangle may be thought as a closed figure which has only three straight lines as its sides. End point of first line is connected to start point of second line, end point of second line is connected to start point of third line and end point of third line is connected to start point of first line. At the points where start point and end point of any two lines meet an angle is formed and this angle opens towards inner side. Thus three angles are formed inside a triangle. Hence figure is referred to as triangle.
Every area on a surface having three straight lines as its sides is referred to as triangular area.
          
A triangle is a closed figure with three sides. It has three interior angles. On the basis of comparative lengths of sides and measurement of angles, triangles can be classified as under:
Name
Description
Figure or shape of triangle
Equilateral Triangle Triangle of which all three sides are of equal length.
Isosceles Triangle Triangle of which two sides are of equal length.
Scalene triangles
Triangle of which all three sides are of different lengths.
Acute Triangle
Triangle of which all interior angles are less than 90 degrees. All interior angles are acute angles.
Obtuse Triangle
Triangle of which one angle is obtuse angle. Obtuse angle is greater than 90 degrees.
Right Triangle
Triangle of which one angle is right angle (90 degrees)
 

DEFINITIONS OF SOME WORDS USED IN REGERENCE TO A TRIANGLE

 
Vertex of a triangle
Vertex of a triangle is the point at which two sides of a triangle meet.
Altitude of a triangle
Altitude of a triangle is the perpendicular segment from a vertex of a triangle to the line containing the opposite side.
Base of a triangle
Base of a triangle is the side of a triangle to which an altitude is drawn.
Height of a triangle
Height of a trianble is the length of an altiutde.
 
DEFINITIONS OF SOME WORDS USED IN REGERENCE TO TWO TRIANGLES
Term
Definition
Figures or shapes
Congruent Triangles
Congruent triangles are exactly the same. They have the same corresponding side lengths and angle measures. There are absolutely no differences between them. The symbol is the = with the ~ on top.
   In case of congruent triangles, shape and size of triangles is the same. If one is put on top of other it covers totally. Corresponding sides are of equal length. Their areas are also equal.
Similar Triangles
Similar triangles have the same corresponding angle measurements, but their corresponding sides are only proportional. For example, let's say a small triangle was similar to a larger triangle. A side of the small triangle is 2 and the corresponding side on the bigger triangle is 4. This means that the bigger triangle is 2 times bigger than the smaller one (2 * 2 = 4). So since they are similar, all of the sides of the bigger triangle will be 2 times larger than the corresponding sides of the smaller triangle. The symbol for similarity is ~.
They have similar shapes but they are unequal in size. Ratio in legths of corresponding sides is either less than 1 or greater than one. Their area a are unequal.
 

TO BE CONTINUED ...