Question

line m is the line of reflection that takes triangle def onto triangle def. determine if each statement is true or false.
the line ee is parallel to the line ff.
the line dd is perpendicular to line m.
the line segment connecting f to the line segment connecting f to the line of reflection is congruent.
the line segment connecting e to the line segment connecting e to the line of reflection is congruent.
the line segment connecting d to the line of reflection is congruent to the line segment connecting d to the line of reflection.
line segment df is congruent to line segment df.
line m is the perpendicular bisector of ff.
triangle def is congruent to triangle def.
line segment ee is congruent to line segment dd.
line ed is parallel to ed

Explanation:

Step1: Recall properties of reflection

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

Step2: Analyze each statement

• The line $EE'$ is parallel to the line $FF'$: True. Since the distance from each point on $\triangle DEF$ to the line of reflection $m$ is the same as the distance from its image point to the line of reflection $m$, the lines connecting corresponding points ($EE'$ and $FF'$) are parallel.
• The line $DD'$ is perpendicular to line $m$: True. The line of reflection $m$ is the perpendicular - bisector of the segment $DD'$.
• The line segment connecting $F$ to the line $m$ is congruent to the line segment connecting $F'$ to the line $m$: True. This is a property of reflection. The distance from a point to the line of reflection is the same as the distance from its image point to the line of reflection.
• The line segment connecting $E$ to the line $m$ is congruent to the line segment connecting $E'$ to the line $m$: True. By the definition of reflection, the line of reflection is equidistant from a point and its image.
• The line segment $DF$ is congruent to the line segment $D'F'$: True. Reflection is a rigid transformation, and rigid transformations preserve distance, so corresponding line segments in the pre - image and image are congruent.
• Line $m$ is the perpendicular bisector of $FF'$: True. This is a fundamental property of reflection.
• $\triangle DEF$ is congruent to $\triangle D'E'F'$: True. Reflection is a rigid transformation that preserves shape and size, so the pre - image and image triangles are congruent.
• The line segment $EE'$ is congruent to the line segment $DD'$: False. There is no guarantee that the distances between corresponding points (like $E$ and $E'$ and $D$ and $D'$) are the same in terms of length of the segments connecting them.
• Line $ED$ is parallel to $E'D'$: True. Since reflection is a rigid transformation that preserves angle measures, corresponding lines in the pre - image and image are parallel.

Answer:

True, True, True, True, True, True, True, False, True