Question

describing the properties of a reflection. consider the reflection of △abc across the line of reflection, pt. which statements must be true? choose four correct answers. $overline{aa}paralleloverline{bb}$, $cq = qc$, $aa = cc$, $overleftrightarrow{pt}perpoverline{aa}$

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 $\overline{A'A}\parallel\overline{B'B}$: In a reflection, the segments connecting pre - image and image points are not necessarily parallel. This statement is false.
• For $C'Q = QC$: Since the line of reflection $\overleftrightarrow{PT}$ is the perpendicular - bisector of the segment connecting a point and its image, if $Q$ is the intersection of $\overleftrightarrow{PT}$ and $\overline{C'C}$, then $C'Q=QC$. This statement is true.
• For $A'A = C'C$: The lengths of the segments connecting pre - image and image points are not necessarily equal. This statement is false.
• For $\overleftrightarrow{PT}\perp\overline{A'A}$: The line of reflection is perpendicular to the segments connecting pre - image and image points. So $\overleftrightarrow{PT}\perp\overline{A'A}$. This statement is true.

Answer:

$C'Q = QC$, $\overleftrightarrow{PT}\perp\overline{A'A}$ (assuming we need to just identify two correct ones as the problem - solving process shows these are true. If we must choose four, more information about the figure's properties would be needed. But based on basic reflection properties, these two are always true for a reflection over $\overleftrightarrow{PT}$)