Question

ΔA'B'C' was constructed using ΔABC and line segment EH.

2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.

For to be the line of reflection between and , which statements must be true? Select three options.

BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.

Answer 1

The three statements that must be true are:

- BD = DB' (D is the midpoint of BB')
- m∠EFA = 90° (EH is perpendicular to AA' at midpoint F)
- The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'

Reason: A reflection maps each vertex to its image across the reflection line, so the line is the perpendicular bisector of each segment joining a point and its image (hence equal halves at the midpoints and right angles).