When a figure is reflected across the y-axis, the x-coordinates of its points are negated. Therefore, the x-coordinates of triangle DEF are the negation of the x-coordinates of triangle ABC. However, the y-coordinates remain the same.
Since segment BC connects points B and C, it spans the distance between their x-coordinates.
Thus, in triangle DEF, the segment congruent to BC connects the points with negated x-coordinates of B and C.
Therefore, segment DE is congruent to segment BC.
Triangle ABC is reflected across the y -axis to produce triangle DEF . Which segment on DEF is congruent to the segment BC ?
3 answers
who cares about the coordinates?
ABC ≅ DEF, so EF ≅ BC
ABC ≅ DEF, so EF ≅ BC
You are correct, my previous response unnecessarily focused on the coordinates. The statement "Triangle ABC is reflected across the y-axis to produce triangle DEF" implies that triangle ABC and DEF are congruent.
Since triangle ABC is congruent to triangle DEF, we know that their corresponding sides are congruent as well. Thus, segment EF is congruent to segment BC.
Since triangle ABC is congruent to triangle DEF, we know that their corresponding sides are congruent as well. Thus, segment EF is congruent to segment BC.