Question

consider the reflection of △abc across the line of reflection, (overleftrightarrow{pt}). which statements must be true? check all that apply. aa = cc cq = qc (overleftrightarrow{pt}perpoverline{aa}) (overline{cc}perpoverline{bb}) (overline{aa}paralleloverline{bb}) (mangle trb = 90^{circ})

Explanation:

Step1: Recall reflection properties

In a reflection, the line of reflection is the perpendicular - bisector of the segments joining pre - image and image points.

Step2: Analyze "C'Q = QC"

Since the line of reflection \(PT\) is the perpendicular - bisector of \(CC'\), the distance from \(C'\) to the line of reflection at point \(Q\) is equal to the distance from \(C\) to the line of reflection at point \(Q\), so \(C'Q = QC\).

Step3: Analyze "PT⊥AA'"

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

Step4: Analyze "m∠TRB = 90°"

Since \(PT\) is the line of reflection and \(B\) and \(B'\) are related by reflection, and \(PT\) is perpendicular to \(BB'\), and \(R\) lies on \(PT\), \(m\angle TRB=90^{\circ}\).

Step5: Analyze other statements

• \(A'A\) and \(C'C\) are not necessarily equal in length.
• \(CC'\) and \(BB'\) are not necessarily perpendicular.
• \(AA'\) and \(BB'\) are not necessarily parallel.

Answer:

C'Q = QC, PT⊥AA', m∠TRB = 90°