1. In Fig - 1, ABC is an isosceles triangle in which \(AB = AC\). E is a point on the side CB produced such that \(FE \bot AC\). If \(AD \bot CB\), prove that \(AB × EF = AD × EC\).

2. In Fig - 2, \(\angle D = \angle E\) and \(\frac{AD}{DB}=\frac{AE}{EC}\). Prove that BAC is an isosceles triangle.

3. In Fig - 3, PQR is a right triangle right-angled at P and PS ⊥ QR . If PQ =6 cm and QS = 4 cm, find the PS, RS and PR. 

4. In Fig. 4, \(DE//BC\) and \(AD:DB =5:4\). Find \(\frac{Area(\triangle{DEF})}{Area(\triangle{CFB})}\).

5. In Fig - 5, ABC is a right triangle, right-angled at C and D is the mid-point of BC. Prove that \(AB^2 = 4AD^2 - 2AC^3\).

******************************End*********************************