Question

In the figure, it is given that RT = TS, $\angle 1=2\angle 2and\angle 4=2\angle 3.Provethat\Delta RBT\cong SAT.$

Answer 1

Given : In the figure, RT = TS

$\angle 1=2\angle 2and\angle 4=2\angle 3$

To Prove : $\Delta RBT\cong SAT$

Proof : $\because \angle 1=\angle 4$

(Vertically opposite angles)

But $\angle 1=2\angle 2and4=2\angle 3$

$\therefore 2\angle 2=2\angle 3\Rightarrow \angle 2=\angle 3$

$\because RT=ST$ (Given)

$\therefore \angle R=\angle S$

(Angles opposite to equal sides)

$\therefore \angle R-\angle 2=\angle S-\angle 3$

$\Rightarrow \angle TRB=\angle AST$

Now in $\Delta RBTand\Delta SAT$

$\angle TRB=\angle SAT$ (Proved)

RT = ST (Given)

$\angle T=\angle T$ (Common)

$\therefore \Delta RBT\cong SAT$ (SAS axiom)