NCERT Class 9 Mathematics

118 MATHEMATICS

Observe that the triangles may or may not be congruent to each other.
So, equality of three angles is not sufficient for congruence of triangles. Therefore,
for congruence of triangles out of three equal parts, one has to be a side.

Let us now take some more examples.

Example 3 : Line-segment AB is parallel to another line-segment CD. O is the
mid-point of AD (see Fig. 7.15). Show that (i) ✂AOB ☎✂DOC (ii) O is also the
mid-point of BC.

Solution : (i) Consider ✂AOB and ✂DOC.

✄ABO =✄DCO

(Alternate angles as AB || CD

and BC is the transversal)

✄AOB =✄DOC

(Vertically opposite angles)

OA = O D (Given)

Therefore, ✂AOB ☎✂DOC (AAS rule)

(ii) OB = O C (CPCT)

So, O is the mid-point of BC.

EXERCISE 7.1

1. In quadrilateral ACBD,
   AC = AD and AB bisects A
   (see Fig. 7.16). Show that ✁ABC ✆✁ABD.
   What can you say about BC and BD?

Fig. 7.15

Fig. 7.16