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11/07/2021 11:35 am
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In quadrilateral ACBD, AC = AD and AB bisect A (see Fig.). Show that ΔABC ΔABD. What can you say about BC and BD?
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11/07/2021 11:36 am
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.