Question

consider the reflection of δabc 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 reflection properties

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

Step2: Analyze each statement

• For $A'A = C'C$: There is no guarantee that the distances from $A$ to $A'$ and $C$ to $C'$ are equal just based on reflection. This is false.
• For $C'Q=QC$: Since the line of reflection $\overleftrightarrow{PT}$ is the perpendicular - bisector of the segment $\overline{C'C}$, and $Q$ lies on the line of reflection, $C'Q = QC$. This is true.
• For $\overleftrightarrow{PT}\perp\overline{A'A}$: The line of reflection is perpendicular to the line segment connecting a point and its image. So $\overleftrightarrow{PT}\perp\overline{A'A}$. This is true.
• For $\overline{C'C}\perp\overline{B'B}$: There is no reason for $\overline{C'C}$ and $\overline{B'B}$ to be perpendicular. This is false.
• For $\overline{A'A}\parallel\overline{B'B}$: Since the line of reflection is perpendicular to both $\overline{A'A}$ and $\overline{B'B}$, $\overline{A'A}\parallel\overline{B'B}$. This is true.
• For $m\angle TRB = 90^{\circ}$: There is no information to suggest that $\angle TRB$ is a right - angle. This is false.

Answer:

$C'Q = QC$, $\overleftrightarrow{PT}\perp\overline{A'A}$, $\overline{A'A}\parallel\overline{B'B}$