Question

select the transformation that maps the figure onto itself. a a reflection over an altitude of the triangle. b a reflection over a horizontal line passing through the midsegment of the triangle. c a 180 degree rotation clockwise about the center of the triangle. d a 90 degree rotation counterclockwise

Explanation:

An equilateral triangle (which this appears to be) has symmetry. A reflection over an altitude (which is also a median and angle - bisector) maps the triangle onto itself.

• For option B: A reflection over a horizontal line through the mid - segment will not map the triangle onto itself as the top and bottom parts are not mirror images in that way.
• For option C: A \(180^{\circ}\) rotation of an equilateral triangle about its center will not map it onto itself (a \(120^{\circ}\) rotation would).
• For option D: A \(90^{\circ}\) rotation of an equilateral triangle will not map it onto itself.

Answer:

A. A reflection over an altitude of the triangle.