Question

Maria drew two parallel lines kl and mn intersected by a transversal pq, as shown below: two parallel lines kl and mn with pq as a transversal intersecting kl at point r and mn at point s. angle krs is shown congruent to angle msq. which fact would help maria prove that the measure of angle krq is equal to the measure of angle msq?

Answer 1

${\text{Here, two parallel lines }}kl\,{\text{and }}mn\,{\text{are intersected by a}} \hfill \\ {\text{transversal }}pq\,{\text{at points }}r\,{\text{and }}s\,{\text{respectively}}{\text{. }} \hfill \\ {\text{Here, two angles }}krq\,{\text{and}}\,msq\,{\text{formed}}\,{\text{by the transversal }}pq\,{\text{with respect to the lines}} \hfill \\kl\,{\text{and }}mn\,{\text{such that}} \hfill \\ m\left( {\angle \;krq} \right)\, = \,m\left( {\angle \;msq} \right) \hfill \\

text{as these two angles are corresponding angles which are always of equal measure,}} \hfill \\

{\text{i}}{\text{.e}}{\text{., corresponding angles are always congruent to each other}}{\text{.}} \hfill$

Answer 2

Vertical angles MSQ and RSN are equal, and alternate interior angles KRS and RSN are equal.