Question

Statements in the List I have to be matched with statements in the List II.

Answer 1

(A) $A{B}^2=A{C}^2+B{C}^2$

Since, $△ABC$ is an isosceles right angled triangle.

$\therefore AC=BC$

Now, $A{B}^2=A{C}^2+A{C}^2=2A{C}^2$

(B) $\frac{area\left(△ABC\right)}{area\left(△DEF\right)}=\frac{(AB{)}^2}{(DE{)}^2}=\frac{(1.2{)}^2}{(1.4{)}^2}=\frac{1.44}{1.96}$

$=\frac{36}{49}=\frac{(36\times 2)}{(49\times 2)}=\frac{72}{98}$

(C) $\frac{area\left(△ABC\right)}{area\left(△APQ\right)}=\frac{(BC{)}^2}{(PQ{)}^2}=\frac{36}{49}$

$\frac{BC}{PQ}=\frac{6}{7}$

(D) $\because DE\parallel BC$

$\therefore \frac{AD}{DB}=\frac{AE}{EC}=\frac{6}{7}$