Question

which transformation shows a reflection of δdef?

Explanation:

To determine which transformation is a reflection of \(\triangle DEF\), we analyze the properties of a reflection (a flip over a line, creating a mirror image with corresponding sides and angles equal, and the figure being congruent and symmetric with respect to the line of reflection).

Step 1: Recall Reflection Properties

A reflection preserves the shape, size (congruent), and the orientation is mirrored (like a mirror image). Corresponding sides and angles match, and the figure is symmetric across the line of reflection.

Step 2: Analyze Each Option

• First Option (Green and Gray Triangles): The triangles appear to be rotated or translated, not mirrored (e.g., right angle in \(\triangle D'E'F'\) vs. no right angle in \(\triangle DEF\)).
• Second Option (Purple and Light Purple Triangles): \(\triangle D'E'F'\) is a mirror image of \(\triangle DEF\): corresponding sides (marked with ticks) match, angles (including the right angle) align as a reflection, and the orientation is flipped (like a mirror).
• Third Option (Blue Triangles): The triangles appear to be rotated (e.g., vertex order \(F, E, D\) vs. \(F', E', D'\) suggests rotation, not reflection).

Answer:

The second transformation (with the purple \(\triangle DEF\) and light purple \(\triangle D'E'F'\)) shows a reflection. (Identify the option with the mirror - image triangle, typically the middle one in the given diagram.)