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.
To determine if the triangles remain congruent after a translation, we need to consider the congruency requirements. The congruent triangles in question are ΔABC and ΔDEF, and they are congruent by the Side-Side-Side (SSS) criterion. According to the SSS criterion, for two triangles to be congruent, their corresponding sides must be equal in length.
Now, let's analyze the given translation. ΔABC is translated 2 units to the left and 3 units down. This means that every point in ΔABC is moved 2 units to the left and 3 units down to obtain the corresponding point in ΔDEF.
Under a translation, the lengths of the sides of a shape remain the same. Therefore, the corresponding sides of ΔABC and ΔDEF remain equal in length. Translations only affect the position of the shape in the coordinate plane, not its shape or size.
Hence, even after the translation, ΔABC and ΔDEF will remain congruent since the Side-Side-Side criterion is still satisfied. The translation of 2 units left and 3 units down does not change the lengths of the sides, so the triangles maintain their congruence.
Damon already answered this for you.
The sides have not changed length, so the triangles are still congruent.
Think about it. Cut out a triangle and then move it around. Has it changed shape in any way?