Question

Explain why ADEF-AXYZ. D E + F 3 Z -3 -2 X

Answer 1

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

`YZ=\sqrt[]{0.5^(2)+0.5^(2)}=\sqrt[]{0.5}=0.707`

The length of the segment DE is 4 units.

The length of the segment EF is:

`EF=\sqrt[]{1^(2)+1^(2)}=\sqrt[]{2}=1.414`

You can notice that DE = 2XY and EF = 2YZ, the same happens for DF and XZ.

Hence, triangle DEF is congruent to triangle XYZ.