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Example 16: In which of the following figures:
p q
r

B
A M C N D
E O F

(i) (ii) (iii)
(a) perpendicular bisector is shown? (b) bisector is shown?

(c) only bisector is shown? (d) only perpendicular is shown?
Solution: From the given figures, we can find that p ⊥ AB but AM ≠ MB; q ⊥ CD and CN = ND;
EO = OF but r is not perpendicular to EF. Therefore,

(a) the perpendicular bisector is shown in (ii) only.
(b) the bisector is shown in both (ii) and (iii).
(c) the only bisector is shown in (iii). (d) the only perpendicular is shown in (i).

Enrichment

Pair of Angles
There are some angles which are always in pairs. Here is the list of some important pairs of angles.
(a) Complementary angles: When two angles sum up to 90°, they are
called complementary angles. For example, 30° and 60°; 50° and
50°
40° are pairs of complementary angles. 60°
30° 40°
(b) Supplementary angles: When the sum of two angles is 180°, they are called supplementary angles.

For example, 115° and 65°; 130° and 50° are pairs of supplementary angles.

65°
115° 130°
50°
(c) Adjacent angles: Two angles that have a common vertex, a common arm and the non-common
arms are on opposite sides of the common arm are adjacent angles.
For example, in the given figure ∠1 and ∠2 are adjacent angles.

Common Common arm
Vertex
1
2
(d) Vertically opposite angles: When two lines intersect each other at a point,
there are four vertical angles formed. The angles which are not adjacent are 4 1 2
called vertically opposite angles. They are equal to each other. 3

Here, ∠1 = ∠3 and ∠2 = ∠4 are vertically opposite angles.

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