Question

which of these triangles are reflections of △ abc?
options:
○ △ kmn is a reflection of △ abc.
○ △ def, △ ghj, and △ kmn are reflections of △ abc.
○ △ def and △ ghj are reflections of △ abc.
○ △ def is a reflection of △ abc.
○ △ ghj is a reflection of △ abc.

Explanation:

Step1: Recall Reflection Properties

A reflection of a figure over a line (like y - axis or x - axis) should be a mirror image, with corresponding points equidistant from the line of reflection.

Step2: Analyze Each Triangle

• For \(\triangle DEF\): Visually, it appears to be a reflection of \(\triangle ABC\) over the y - axis (since the x - coordinates of corresponding points are negatives, and y - coordinates are similar).
• For \(\triangle GHJ\): It appears to be a reflection of \(\triangle ABC\) over the x - axis (since the y - coordinates of corresponding points are negatives, and x - coordinates are similar).
• For \(\triangle KMN\): The shape and orientation do not match the mirror - image property of a reflection of \(\triangle ABC\). So \(\triangle DEF\) and \(\triangle GHJ\) are reflections of \(\triangle ABC\).

Answer:

\(\triangle DEF\) and \(\triangle GHJ\) are reflections of \(\triangle ABC\) (the option: \(\triangle DEF\) and \(\triangle GHJ\) are reflections of \(\triangle ABC\)).