Question

Question 4
In figure, $BA\perp AC,DE\perp DF$ such that BA =DE and BF =EC. Show that $\Delta ABC\cong \Delta DEF$

Answer 1

Given in figure,
$BA\perp AC,DE\perp DF$ such that BA = DE and BF = EC
To show : $\Delta ABC\cong \Delta DEF$
Proof :
Since BF =EF
On adding CF both side, we get
BF +CF = EC +CF
$\Rightarrow BC=EF...\left(i\right)$
In $\Delta ABC$ and $\Delta DEF\angle A=\angle D={90}^{\circ }[\because BA\perp AC$ and $CE\perp DF]$
BC = EF [from Eq.(i)]
and AB = DE [given]
$\therefore \Delta ABC\cong \Delta DEF$ [by RHS congruence rule]