ANGLES PART III

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 ഽ shapes . The F shape gives two equal angels called corresponding angles. The Z or  ഽ  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.