Question 1141085
an isometry is a transformation that presrves shape and size.


in other words, the transformed figure is congruent to the original figure.


if triangle DEF is generated from triangle ABC by some isometry, then triangle DEF is congruent to triangle ABC.


if triangle XYZ is generated from triangle DEF by some isometry, then triangle XYZ is contruent to triangle DEF.


you have:


triangle DEF is congruent to triangle ABC.


triangle XYZ is congruent to triangle DEF.


therefore, you have triangle ABC is congruent to triangle DEF which is congruent to triangle XYZ.


therefore, you can say that triangle ABC is congruent to triangle XYZ.


this is called the Transitive Property of Congruence.


here's a reference on properties of equality and congruence.


<a href = "https://bp025.k12.sd.us/images/Math_Links/ALGEBRAIC%20PROPERTIES%20OF%20EQUALITY2.htm" target = "_blank">https://bp025.k12.sd.us/images/Math_Links/ALGEBRAIC%20PROPERTIES%20OF%20EQUALITY2.htm</a>