Question

the image of △abc after a reflection across eg is △abc. which triangle must be a right triangle and why? △bcc is right because b lies of the line of reflection. △bgc is right because eg ⊥ cc. △abc is right because it is the image of △abc. △adc is right because aa intersects ac at a

Explanation:

Step1: Recall reflection property

When a figure is reflected across a line, the line of reflection is the perpendicular - bisector of the segments connecting corresponding points. In the case of reflecting $\triangle ABC$ across $\overleftrightarrow{EG}$ to get $\triangle A'B'C'$, the line $\overleftrightarrow{EG}$ is the perpendicular - bisector of $CC'$.

Step2: Analyze right - angle in triangles

In $\triangle BGC$, since $\overleftrightarrow{EG}\perp\overline{CC'}$, the angle formed at the intersection of $\overleftrightarrow{EG}$ and $\overline{CC'}$ (which is part of $\triangle BGC$) is a right angle.

Answer:

$\triangle BGC$ is right because $\overleftrightarrow{EG}\perp\overline{CC'}$.