Question

Square ABCD is shown below.

Triangle A-B-C has a line drawn from the angle A to the midpoint D on the side B-C. Angle A-B-D is labeled as b and angle A-C-D is labeled as c.

Square ABCD is reflected about side BC. Which of the following statements are true? Select three that apply.
A.
Vertex B is the midpoint of AA'.

B.
Side BC is parallel to AA'.

C.
The length of CD is equal to the length of C'D'.

D.
Vertex C and vertex C' are located at the same point.

Answer 1

A, C, and D.

- A: True. B lies on the mirror line BC and AB is perpendicular to BC, so under reflection B is the midpoint of AA'.
- B: False. AA' is perpendicular to the mirror line BC, not parallel to it.
- C: True. Reflection is an isometry, so corresponding segment lengths are equal: CD = C'D'.
- D: True. C lies on the mirror line BC, so it maps to itself (C' = C).