Question

triangle abc is congruent to △abc by the hl theorem. what single rigid transformation maps △abc onto △abc?
options:
○ dilation
○ reflection
○ rotation
○ translation

Explanation:

1. Recall the definitions of rigid transformations:

• Dilation is not a rigid transformation as it changes the size (scales the figure), so we can eliminate dilation.
• Reflection is a transformation that flips a figure over a line (the line of reflection). Looking at the triangles, if we consider the line through point \( B \) (the common vertex), reflecting \( \triangle ABC \) over the line containing \( B \) (or a vertical/horizontal line depending on the orientation) would map \( A \) to \( A' \) and \( C \) to \( C' \) since the triangles are congruent right triangles with \( B \) as a common vertex.
• Rotation would involve turning the figure around a point, but the orientation and position suggest a flip (reflection) rather than a rotation.
• Translation is a slide, but the triangles are not "slid" but rather flipped relative to a line through \( B \).

1. Analyze the given triangles: \( \triangle ABC \) and \( \triangle A'BC' \) share the vertex \( B \), and the right angles are on opposite sides of the segment \( BC \) (or \( BC' \)). This is consistent with a reflection over the line containing \( B \) (or the angle bisector, or a vertical line through \( B \)) which would map one triangle to the other.

Answer:

B. reflection