Question

Consider the reflection of ΔABC across the line of reflection, Line P T.

2 right triangles are shown. Line P T is the line of reflection. Line segment A prime A has a midpoint at point S. Line segment B prime B has a midpoint at point R. Line segment C prime C has a midpoint at point Q.
Which statements must be true? Check all that apply.

A'A = C'C
C'Q = QC
Line P T⊥ A'A
C'C ⊥ B'B
A'A || B'B
m∠TRB = 90°

Answer 1

True:
- C'Q = QC (Q is the midpoint of C'C)
- Line PT ⟂ A'A (the mirror is the perpendicular bisector of AA')
- A'A || B'B (AA' and BB' are both perpendicular to PT, so they are parallel)
- m∠TRB = 90° (TR lies on PT and RB lies along BB', so they meet at right angle)

False:
- A'A = C'C (not necessarily equal unless A and C are the same distance from PT)
- C'C ⟂ B'B (both are perpendicular to PT, so they are parallel, not perpendicular)