Section A: Board level Questions
- State and prove the Basic Proportionality Theorem (Thales Theorem).
- In a right triangle $ABC$, right-angled at $B, if $D$ is the mid-point of $BC, prove that $AC^2 = AD^2 + 3CD^2$.
- In $\triangle ABC$, $DE \parallel BC$ intersecting $AB$ at $D$ and $AC$ at $E. If $AD = x, $DB = x-2, $AE = x+2, and $EC = x-1, find the value of $x$.
- Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
- State the similarity criteria of triangles (AAA, SAS, SSS).
