PROPERTIES OF PARALLEL LINES
The idea of parallel lines is very important in geometry. In Fig 18.4, AB and CD are two parallel lines. They are crossed by a slanting or oblique line EF, called a transversal since it cuts parallel lines.
This gives rise to F and Z shapes or à´½ shapes . The F shape gives two equal angels called corresponding angles. The Z or  à´½  shape gives two equal angles called alternate angels.


1. The angels B and F are called corresponding angels. Also A and E are corresponding angels.
Corresponding abgels are equal. i.e. b=f, a=e, d=h, and c= g.

2. The angels C and F are called alternate angels. Also D and E are alternate angels.
Alternate angels are equal. i.e. c=f and d=e.

3. The angels C and E are called co- interior angels. Also D and F are co- interior angels.
Co-interior angels add up to 180°. i.e. d+f= 180° and c+e= 180°


EXAMPLE
Calculate the size of the lettered angels in the diagrams below.

SOLUTION
a=40° ( Corresponding a angles are equal)
b=40° ( Alternate angels are equal)
a+c=180°
→40+c=180°
→ c=180°-40° =140°.

ASSIGNMENT
Find the size of the angels marked I,H,J.