Question

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

Answer 1

Answer:

Solution:

It is given that AC and AD are equal i.e. AC = AD and the line segment AB bisects A.

We will have to now prove that the two triangles ABC and ABD are similar i.e. ΔABC ΔABD

Proof:

Consider the triangles ΔABC and ΔABD,

(i) AC = AD (It is given in the question)

(ii) AB = AB (Common)

(iii) CAB = DAB (Since AB is the bisector of angle A)

So, by SAS congruency criterion, ΔABC ΔABD.

For the 2nd part of the question, BC and BD are of equal lengths by the rule of C.P.C.T.