Question

the image of △abc after a reflection across eg is △abc. which triangle must be a right triangle and why? △adc is right because aa intersects ac at a. △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.

Explanation:

Step1: Recall reflection property

In a reflection, the line of reflection is perpendicular to the segment joining a point and its image. Here, $\overleftrightarrow{EG}$ is the line of reflection and $\overline{CC'}$ is a segment joining a point $C$ and its image $C'$. So $\overleftrightarrow{EG}\perp\overline{CC'}$. In $\triangle BGC$, one of the angles is $90^{\circ}$ due to this perpendicular - relationship.

Answer:

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