Question

Identify any congruent figures in the coordinate plane.

Answer 1

Check the congruency of figure.

Given, figure

From the figure we observe for square ABCD and EFGH, we get:

For lines,

$\mathrm{AB}=\mathrm{EF},\mathrm{BC}=\mathrm{FG},\mathrm{CD}=\mathrm{GH},\mathrm{DA}=\mathrm{HE}$

And, for angles,

$\angle \mathrm{A}=\angle \mathrm{E},\angle \mathrm{B}=\angle \mathrm{F},\angle \mathrm{C}=\angle \mathrm{G},\angle \mathrm{D}=\angle \mathrm{H}$

As we know that if all the corresponding sides and angles of two figures are equal then both the figures are congruent.

So, Square ABCD and EFGH are congruent.

Similarly for squares RSTU and IJKL, we get

For lines,

$\mathrm{RS}=\mathrm{IJ},\mathrm{ST}=\mathrm{JK},\mathrm{TU}=\mathrm{Kl},\mathrm{UR}=\mathrm{LI}$

And, for angles,

$\angle \mathrm{R}=\angle \mathrm{I},\angle \mathrm{S}=\angle \mathrm{J},\angle \mathrm{T}=\angle \mathrm{K},\angle \mathrm{L}=\angle \mathrm{U}$

As we know that if all the corresponding sides and angles of two figures are equal then both the figures are congruent.

So, Square RSTU and IJKL are congruent.

Hence, square ABCD is congruent to EFGH and square RSTU is congruent to IJKL.