Question

consider the reflection of △abc across the line of reflection, pt. which statements must be true? check all that apply. aa = cc cq = qc pt⊥aa cc⊥bb aa∥bb m∠trb = 90°

Explanation:

Step1: Recall properties of reflection

In a reflection across a line, the line of reflection is the perpendicular - bisector of the segment joining a point and its image.

Step2: Analyze \(C'Q = QC\)

Since line \(\overleftrightarrow{PT}\) is the line of reflection, it bisects the segment \(\overline{C'C}\), so \(C'Q = QC\).

Step3: Analyze \(\overleftrightarrow{PT}\perp\overline{A'A}\)

The line of reflection \(\overleftrightarrow{PT}\) is perpendicular to the segment joining a point \(A\) and its image \(A'\), so \(\overleftrightarrow{PT}\perp\overline{A'A}\).

Step4: Analyze other statements

• For \(A'A = C'C\), there is no reason to assume that the distances from \(A\) to \(A'\) and \(C\) to \(C'\) are equal just based on the reflection property.
• \(\overline{C'C}\) and \(\overline{B'B}\) are not necessarily perpendicular.
• \(\overline{A'A}\) and \(\overline{B'B}\) are not necessarily parallel.
• There is no information to suggest that \(m\angle TRB=90^{\circ}\).

Answer:

C'Q = QC, \(\overleftrightarrow{PT}\perp\overline{A'A}\)