Question

write an indirect proof of the converse of the corresponding angles theorem following the outline below. given: ∠1≅∠2 prove: ℓ||n assume ℓ is not parallel to n. then it is possible to construct a line m that is parallel to ℓ and passes through the intersection of lines ℓ and n. since line m and line n intersect and are not parallel to each other, m∠3 (do not include the degree symbol in your answer.)

Explanation:

Step1: Consider properties of parallel lines

Si $m\parallel\ell$ y $\angle1\cong\angle2$, por el teorema de ángulos correspondientes, $\angle1 = \angle3$ (ya que $\angle1$ y $\angle3$ son ángulos correspondientes para $m\parallel\ell$). Pero si $\ell$ no es paralela a $n$ y $m\parallel\ell$, entonces $m$ y $n$ se intersectan. Entonces, $m\angle3
eq m\angle2$ porque si $\angle3=\angle2$, entonces $n$ sería paralela a $m$ (por el teorema inverso de ángulos correspondientes) y como $m\parallel\ell$, entonces $n\parallel\ell$, lo cual contradiría nuestra suposición inicial.

Answer:

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