Question

KZ and MN are parallel lines. O is the midpoint of segment LM.

Which transformation of the plane can we use to prove angles and are congruent, and why?
A) A translation along the directed line segment ML maps line KZ onto MN and angle [insert angle label] onto angle [insert angle label].
B) A 180-degree rotation about point O maps ray LK onto MN and vice versa, and the same for rays LÒ and [insert the appropriate ray label].
C) A reflection across line KZ maps angle [insert angle label] onto angle [insert angle label].
D) A dilation about point O maps segment LM onto a new segment MN."

Answer 1

A translation along segment ML can be used to prove that angles [insert angle label] and [insert angle label] are congruent.

Step-by-step explanation:

To prove that angles [insert angle label] and [insert angle label] are congruent, we can use transformation A) A translation along the directed line segment ML maps line KZ onto MN and angle [insert angle label] onto angle [insert angle label].

Translation is a transformation that moves every point in a figure the same distance and direction. In this case, a translation along segment ML would move line KZ parallel to MN, and angle [insert angle label] would be mapped onto angle [insert angle label] because the angles are preserved during translation.

Therefore, by performing a translation along segment ML, we can prove that angles [insert angle label] and [insert angle label] are congruent.