Question

from unit 2, lesson 2
triangle hef is the image of triangle hgf after a reflection across line fh.
write a congruence statement for the two congruent triangles.

Explanation:

Step1: Recall the property of reflection

Reflection is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the reflected triangle is congruent to the original triangle.

Step2: Match the vertices

Since triangle \(HEF\) is the reflection of triangle \(HGF\) across line \(FH\), vertex \(E\) corresponds to vertex \(G\), vertex \(H\) corresponds to itself (as it lies on the line of reflection), and vertex \(F\) corresponds to itself (as it lies on the line of reflection).

Answer:

\(\triangle HEF\cong\triangle HGF\)