Question

If $\Delta ABC$ and $\Delta XYZ$ are equilateral triangles and $AB=XY,$ the condition under which $\Delta ABC\cong \Delta XYZ$ is

• A. $ASA$
• B. $RHS$
• C. $SSS$
• D. $AAS$

Answer 1

The correct option is C $SSS$

Given that $\Delta ABC$ and $\Delta XYZ$ are equilateral triangles.

i.e., $AB=BC=CA$

and $XY=YZ=ZX$ …………….$\left(1\right)$

and

here $AB=XY$ ………………$\left(2\right)$

By equation $\left(1\right)$ & $\left(2\right)$

$BC=YZ$ and $CA=ZX$ …………….$\left(3\right)$

We have to show that

$\Delta ABC\cong \Delta XYZ$

In $\Delta ABC$ and $\Delta XYZ$

$AB=XY$ (Given)

$BC=YZ$ (by equation $\left(3\right)$)

$CA=ZX$ (by equation $\left(3\right)$)

So $\Delta ABC\cong \Delta XYZ$ (By $SSS$ rules).