Question

mapping congruent triangles
m is the midpoint of \\(\overline{ad}\\).
what single transformation is required to map one of these congruent triangles onto the other?
options: dilation, reflection, translation, rotation

Explanation:

Step1: Analyze triangle properties

Triangles \( \triangle ABM \) and \( \triangle DCM \) have \( AM = MD \) (M is midpoint), \( BM = CM = 27 \), and \( AB = DC \) (marked congruent). The triangles are on opposite sides of line \( AD \).

Step2: Identify transformation type

A reflection over the line \( AD \) (or the vertical line through M) would map one triangle onto the other, as reflection flips a figure over a line, matching the congruent triangles' positions. Dilation changes size (not here, triangles are congruent), rotation would move around a point (not matching symmetry here), translation slides (not flipping over a line). So reflection is correct.

Answer:

Reflection