Question

In the given figure, 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 is ____.

• A. equal to BF
• B. greater than BF
• C. less than BF
• D. none of these

Answer 1

The correct option is A equal to BF

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

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

$\angle BCF={90}^{\circ }+\angle BCA$

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)