Question

In the figure which of the following given correspondence between the vertices of two triangles are similarity.
(P) correspondence ABC $\leftrightarrow$ DEF
(Q) correspondence ABC $\leftrightarrow$ FDE
(R) correspondence ABC $\leftrightarrow$ EFD

• A. P and R are correct
• B. Only P is correct
• C. Q and R are correct
• D. P, Q and R are correct

Answer 1

The correct option is D P, Q and R are correct

Given that,
$AB=BC=AC$ and $DE=EF=DF$ ........ (1)
In $\Delta ABC$ and $\Delta DEF$,
$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$
$\therefore \Delta ABC\sim \Delta DEF$ by SSS test of similarity,
Thus, the correspondence $ABC\leftrightarrow DEF$

In $\Delta ABC$ and $\Delta FDE$,
$\frac{AB}{FD}=\frac{BC}{DE}=\frac{AC}{EF}$
$\therefore ABC\sim \Delta FDE$ by SSS test of similarity,
Thus, the correspondence $ABC\leftrightarrow FDE$

In $\Delta ABC$ and $\Delta EFD$,
$\frac{AB}{EF}=\frac{BC}{FD}=\frac{AC}{ED}$
$\therefore \Delta ABC\sim \Delta FDE$ by SSS test of similarity,
Thus, the correspondence $ABC\leftrightarrow EFD$

Hence, all P, Q and R are correct.