Question

The image of ΔABC after a reflection across Line E G is ΔA'B'C'.

2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?

ΔA'B'C' is right because it is the image of ΔABC.
ΔADC is right because AA' intersects AC at A.
ΔBCC' is right because B lies of the line of reflection.
ΔBGC is right because Line E G is perpendicular-to CC'.

Answer 1

ΔBGC is right.

Reason: Reflection across line EG means CC' is perpendicular to EG and G is its midpoint. Since B lies on the line of reflection (B = B'), BG lies along EG, so BG ⟂ GC. Thus angle BGC = 90°, so triangle BGC is a right triangle.