Question

△abc was constructed using △abc and line segment eh. for eh to be the line of reflection between △abc and △abc, which statements must be true? select three options. bd = db df = fg m∠efa = 90° the line of reflection, eh, is the perpendicular bisector of bb, aa, and cc. △abc is not congruent to △abc.

Explanation:

Step1: Recall properties of reflection

In a reflection, the line of reflection is the perpendicular bisector of the line - segments connecting corresponding points.

Step2: Analyze option 1

If $\overline{EH}$ is the line of reflection, then for point $B$ and its image $B'$, the line of reflection $\overline{EH}$ bisects $\overline{BB'}$. So, $BD = DB'$. This statement is true.

Step3: Analyze option 2

There is no information given that would suggest $DF=FG$. This statement is not necessarily true based on the properties of reflection.

Step4: Analyze option 3

The line of reflection is perpendicular to the line - segments connecting corresponding points. Since $\overline{AA'}$ is a line - segment connecting a point and its image, and $\overline{EH}$ is the line of reflection, $m\angle EFA = 90^{\circ}$. This statement is true.

Step5: Analyze option 4

By the definition of a reflection, the line of reflection is the perpendicular bisector of the line - segments connecting corresponding points. So, the line of reflection $\overline{EH}$ is the perpendicular bisector of $\overline{BB'}$, $\overline{AA'}$, and $\overline{CC'}$. This statement is true.

Step6: Analyze option 5

A reflection is a rigid transformation, and rigid transformations preserve congruence. So, $\triangle ABC\cong\triangle A'B'C'$. This statement is false.

Answer:

BD = DB', $m\angle EFA = 90^{\circ}$, The line of reflection, $\overline{EH}$, is the perpendicular bisector of $\overline{BB'}$, $\overline{AA'}$, and $\overline{CC'}$