Question

three students attempt to define what it means for $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ to be perpendicular. can you match the teachers comments to the definitions? definition of perpendicular lines teachers comments danielas definition: $overleftrightarrow{ab}$ is perpendicular to $overleftrightarrow{cd}$ if the measure of $angle aoc$ equals the measure of $angle aod$. please rework your definition to use more precise mathematical language. ors definition: $overleftrightarrow{ab}$ is perpendicular to $overleftrightarrow{cd}$ if $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ intersect perfectly sideways. well done! i hadnt previously considered defining perpendicular lines in terms of a rigid transformation like rotation, but by golly it works! kaoris definition: $overleftrightarrow{ab}$ is perpendicular to $overleftrightarrow{cd}$ if one line can be mapped to the other by a rotation about point $o$ of $90^{circ}$. well done! because the measure of $angle cod$ is $180^{circ}$ (by the definition of a straight - angle), the measures of angles $angle aoc$ and $angle aod$ must both be $90^{circ}$.

Explanation:

Daniela's definition is imprecise as just stating two - angle measures are equal doesn't clearly define perpendicularity in a standard way. Or's definition "intersect perfectly sideways" is too informal. Kaori's definition using rotation of 90° is a valid and formal way to define perpendicular lines in terms of transformation.

Answer:

Daniela's definition - Please rework your definition to use more precise mathematical language.
Or's definition - Please rework your definition to use more precise mathematical language.
Kaori's definition - Well done! Because the measure of ∠COD is 180° (by the definition of a straight angle), the measures of angles ∠AOC and ∠AOD must both be 90°.