Statements that must be true:
B. Line l bisects segment CC’.
D. Line BB’ is perpendicular to line l.
F. Triangles ABC and A’ B’ C’ are congruent.
G. Segment BC is congruent to segment B’ C’.
H. The distance from point A to line l is the same as the distance from point A’ to line l.
- B: In a reflection, corresponding points are equidistant from the line of reflection. So, line l bisects segment CC’.
- D: In a reflection, the line of reflection is perpendicular to the segment connecting corresponding points. Therefore, line BB’ is perpendicular to line l.
- F: Reflection preserves shape and size, so triangles ABC and A’ B’ C’ are congruent.
- G: Reflection also preserves lengths, so segment BC is congruent to segment B’ C’.
- H: The distance from a point to a line is the perpendicular distance, and in a reflection, this distance is preserved.
Statements A, C, and E are not necessarily true based on the information provided.
The probable question may be:
Triangle A'B'C' is a reflection of triangle ABC across line l. Select all statements that must be true.
A Line l bisects segment AB.
B Line l bisects segment CC’.
C Angle ABC is 60 degrees.
D Line BB’ is perpendicular to line l.
E Angle ABC is congruent to angle A’ B’ C’.
F Triangles ABC and A’ B’ C’ are congruent.
G Segment BC is congruent to segment B’ C’.
H The distance from point A to line l is the same as the distance from point A’ to line l.