Triangle DEF is congruent to triangle XYZ because triangle DEF is a dilation of triangle XYZ.
The previous can be shown by estimating the dilation scale factor.
The length of segment XY is 2 units.
The length of the segment YZ is
[tex]YZ=\sqrt[]{0.5^{2}+0.5^{2}}=\sqrt[]{0.5}=0.707[/tex]
The length of the segment DE is 4 units.
The length of the segment EF is:
[tex]EF=\sqrt[]{1^{2}+1^{2}}=\sqrt[]{2}=1.414[/tex]
You can notice that DE = 2XY and EF = 2YZ, the same happens for DF and XZ.
Hence, triangle DEF is congruent to triangle XYZ.
