On the coordinate plane, ΔABC ≅ ΔDEF by SSS. ΔABC translates 2 units to the left and 3 units down. Do the triangles remain congruent? Explain why or why not.
please help me
Did you change the length of the sides?
no
To determine if the triangles remain congruent after the translation, we need to understand the concept of congruence and how it applies in this scenario.
Congruent triangles are triangles that have the same shape and size. There are several criteria for proving congruence, including the Side-Side-Side (SSS) criterion you mentioned.
SSS criterion states that if the corresponding sides of two triangles are equal in length, then the triangles are congruent. In this case, you mentioned that ΔABC ≅ ΔDEF by SSS, implying that the corresponding sides of the triangles are equal in length.
Now, let's consider the translation of ΔABC, which moves it 2 units to the left and 3 units down. A translation involves moving an object without changing its shape or size, only its position in the plane. Thus, the translation does not affect the lengths of the sides of ΔABC.
Since the lengths of the corresponding sides of the triangles remain the same, and a translation does not change the size or shape of an object, ΔABC and ΔDEF should remain congruent after the translation. Therefore, the triangles do remain congruent.
To summarize, the triangles remain congruent because the translation does not change the lengths of the corresponding sides.