**In the given figure, ABC and DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that**

**(i) ∆ABD ≅ ∆ACD**

**(ii) ∆ABP ≅ ∆ACP**

**(iii) AP bisects ∠A as well as ∠D**

**(iv) AP is the perpendicular bisector of BC.**

**Solution:**

**More Solutions:**

- AC is its diagonal. Show that
- Show that the quadrilateral formed.
- Prove that CF = 14 AC.
- The straight lines ED and EC.
- Prove that the line segment AD.
- AB || DC, E and F are mid-points of AD and BD.
- Prove that PQRS is a rhombus.
- G is mid-point of CD. Calculate:
- In a ∆ABC, AB = 3 cm, BC = 4 cm and CA = 5 cm.
- If P and Q are mid-points of the sides BC and CD.