Question

ABC is a triangle, right angled at B. If BCDE is a square on the side BC and ACFG is a square on AC, then AD =______ .
(2 Marks)

Answer 1

In $\Delta ACDand\Delta BCF$, we have

$\angle ACD={90}^{\circ }+\angle BCA$ and

$\angle BCF={90}^{\circ }+\angle BCA$ (1 Mark)

CF = CA (Sides of a square)

CD = CB (Sides of a square)

$\therefore \Delta DCA\cong \Delta BCF$
(by SAS congruence rule)

$\Rightarrow AD=BF$ (CPCT) (1 Mark)