Question

can you match the teachers comments to the definitions?
definition of perpendicular lines teachers comments
danielas definition: \\( \overleftrightarrow { a b } \\) is
perpendicular to \\( \overleftrightarrow { c d } \\) if the
measure of \\( \angle a o c \\) equals the
measure of \\( \angle a o d \\).
please rework your definition to use
more precise mathematical language.
oris definition: \\( \overleftrightarrow { a b } \\) is
perpendicular to \\( \overleftrightarrow { c d } \\) if \\( \overleftrightarrow { a b } \\)
and \\( \overleftrightarrow { c d } \\) intersect perfectly
sidcways.
well done! i hadnt previously
considered defining perpendicular
lines in terms of a rigid
transformation like rotation, but by
golly it works!
kaoris definition: \\( \overleftrightarrow { a b } \\) is
perpendicular to \\( \overleftrightarrow { c d } \\) if one
line can be mapped to the
other by a rotation about point
\\( o \\) of \\( 90 ^ { \circ } \\).
well done! because the measure of
\\( \angle c o d \\) is \\( 180 ^ { \circ } \\) (by the definition of
a straight angle), the measures of
angles \\( \angle a o c \\) and \\( \angle a o d \\) must
both be \\( 90 ^ { \circ } \\).

Explanation:

• Daniela's definition: Her description is too vague. She should use more precise mathematical terms like "right - angle" instead of just comparing the measures of two angles in a non - standard way. So, her comment is "Please rework your definition to use more precise mathematical language."
• Ori's definition: Saying "intersect perfectly sideways" is not a valid mathematical term. It is an incorrect and non - mathematical description of perpendicular lines.
• Kaori's definition: Using the concept of rotation (a rigid transformation) to define perpendicular lines is a valid approach. When one line is rotated 90° about the intersection point \(O\) to map to the other line, it is a correct geometric way. So, her comment is related to the rotation concept.

Answer:

• Daniela's definition → Please rework your definition to use more precise mathematical language.
• Ori's definition → (No correct comment as it is an incorrect non - mathematical definition)
• Kaori's definition → Well done! I hadn't previously considered defining perpendicular lines in terms of a rigid transformation like rotation, but by golly it works!