SOLUTION: Suppose that triangle DEF can be generated from triangle ABC by some isometry. Also suppose that triangle XYZ can be generated from triangle DEF by some isometry. From this, we can

Algebra ->  Triangles -> SOLUTION: Suppose that triangle DEF can be generated from triangle ABC by some isometry. Also suppose that triangle XYZ can be generated from triangle DEF by some isometry. From this, we can      Log On


   

Question 1141085: Suppose that triangle DEF can be generated from triangle ABC by some isometry. Also suppose that triangle XYZ can be generated from triangle DEF by some isometry. From this, we can conclude that
ΔABC≅ΔXYZ
.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.

https://bp025.k12.sd.us/images/Math_Links/ALGEBRAIC%20PROPERTIES%20OF%20EQUALITY2.htm