Learn Math [Form 3]

Chapter 1 - Lesson 1

The converse of the statements above is also true:
When a transversal intersects two straight lines, the two lines are parallel if
(a) the corresponding angles are equal,
(b) the alternate angles are equal, and
(c) the sum of the interior angles is 180°.

EXAMPLE 1
In the diagram, all the lines shown are straight lines.

(a) Name the transversals that intersect the two parallel lines.
(b) List the pairs of
      (i) corresponding angles,
      (ii) alternate angles, and
      (iii) interior angles
      between the two parallel lines.

Solution
(a) AB and CD are parallel lines.
     KL, MN and PQ are the transversals.
(b) (i) b and e are corresponding angles.
      (ii) c and f are alternate angles.
      (iii) a and d are interior angles.

Solving problems involving angles associated with transversals

EXAMPLE 2
In the diagram, ABCD is a straight line. What is the value of x?

Solution
BE and CG are parallel lines.
∴ x + 65° = 135°
               x = 135° - 65°
                  = 70°