Parallel Lines and Triangles

Parallel lines and triangle are frequently used terms in geometry and co-ordinate geometry. Here we will learn parallel lines and triangles separately.
Learning parallel lines is very easy. As the name itself indicates that there will be some lines that are parallel to each other. Think logically if two lines are parallel will they ever meet at some point. The answer is no. Because the two parallel lines maintain equal distance between them so there is no chance that they meet at some point. So we can conclude that two lines are parallel if and only if they are coplanar and never meet each other that is maintain they maintain same distance apart.

Transversals:
Transversals are very important while learning parallel lines. Transversal can be defined as a line that intersects two or more  lines, at different points. Simply a line that crosses two or more lines  is called transversal. With the help of transversals we can say whether the two given lines are parallel or not. Figure below shows how a transversal looks.

How can we Know the Lines are Parallel or Not
Answer is with the help of some angles that are formed when transversal passes through pair of coplanar lines. These angles are very important while learning parallel lines.The angles are
• Corresponding Angles
• Alternate Interior Angles
• Alternate Exterior Angles
• Consecutive Interior Angles
• Corresponding angles:
              In our figure the corresponding angles are " a,e " , " d, h" , "b , f" , "c,g".
• Alternate Interior angles:
             The name it self indicates that alternate means on the other side and interior means inner angles. The Alternate Interior angles are "d,f" and "c,e".
• Alternate exterior angles:
      The name it self indicates that alternate means on the other side and exterior means outer angles. Alternate exterior angles in the given figure are "a,g" and "b,h".
• Consecutive interior angles:
          In the given figure consecutive interior angles are "d,e" and "c,f".
Now for two lines to be parallel corresponding angles, alternate Interior angles, alternate exterior angles must be equal and sum of consecutive angles must be equal to 180. Even if one condition is satisfied it is enough as automatically all the other will satisfy. In parallel lines and triangles we have learnt about parallel lines.
Now Lets Learn about Triangles
Triangle is a polygon with three sides and three vertices’. The sum of angles in a triangle is 180º . Figure below shows, how a triangle looks actually. In the triangle below the sum of angles is a + b + c =  180º .

Types of Triangles
There are three types of triangles they are
• Equilateral triangle
• Isosceles triangle.
• Scalene triangle.
In equilateral triangle all the three sides are equal and all the  angles are equal.
In isosceles triangle two sides and their opposite angles are equal.
In scalene all the three sides are not equal.
Figure below shows the different triangles.

This is all about parallel lines and triangles.