Q1. Refer to BPT proof: uses area of triangles sharing heights and bases on parallel lines to prove $\frac{AD}{DB} = \frac{AE}{EC}$.
Q2. Using Pythagoras theorem in right triangles $\triangle ABD$ and $\triangle ABC$ and properties of midpoints.
Q3. By Thales theorem: $\frac{x}{x-2} = \frac{x+2}{x-1} \rightarrow x(x-1) = (x-2)(x+2) \rightarrow x^2-x = x^2-4 \rightarrow x=4$.
Q4. Proof involves expressing area ratio as square of sides ratio, then using similar triangles to relate medians to corresponding sides.
Q5. Define criteria: AAA (angles equal), SAS (two sides in ratio, included angle equal), SSS (all sides in ratio).
