1. 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?
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.
