Angles: An angle is formed by the union of two rays with the common origin. The origin is called vertex and the two rays form two sides of the angle. An angle is denoted by sign <.
Transversal is a line which cuts two or more coplanar (in the same plane) lines in distinct points.
Let AB and CD be two parallel lines and EF be the transversal (as shown in the figure below).
As we can see above, transversal EF cuts AB and CD as a result of various angles are formed (angle a,b,c,d,e,f,g and h as shown in the diagram above).
The following pairs are alternate interior angles:
<c and <f
<d and <e
In case lines AB and CD are parallel, the alternate interior angles are equal to each other.
The following pairs are alternate exterior angles:
<a and <h
<b and <g
In case lines AB and CD are parallel, the alternate exterior angles are equal to each other.
<a = <d; <b = <c; <e = <h; <f= <g
<a and <e
<c and <g
<b and <f
<d and <h
Consecutive interior angles
The following pairs are consecutive interior angles:
<c and <e
<d and <f
In case lines AB and CD are parallel, <c + <e =180° and <d + <f = 180°.
<a and <b are complementary to each other as <a +<b =90° since the points A, O and B constitute a right angle with O as its vertex.