What is the ncert class 9^{th} question of chapter triangles of exercise 7.1 question number 1. Please give me the simplest and easiest solution of this question , also give me the best solution of this question. In quadrilateral ACBD, AC = AD and AB bisect A (see Fig. 7.16). Show that ΔABC ΔABD. What can you say about BC and BD?

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# In quadrilateral ACBD, AC = AD and AB bisect A (see Fig. 7.16). Show that ΔABC ΔABD. What can you say about BC and BD? Q.1

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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 ΔABDProof: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 2

^{nd}part of the question, BC and BD are of equal lengths by the rule of C.P.C.T.