Which can be used to prove that lines l and m are parallel? a) same-side exterior angle theorem b) converse of the alternate interior angles theorem c) converse of the same-side interior angles theorem d) converse of corresponding angles postulate

Option B, C, D

Out of four given options following three options are used to prove line l and m are parallel.

B) Converse of the alternate interior angles theorem  

C) Converse of the same-side interior angles theorem  

D) Converse of corresponding angles postulate

Solution:

Need to check which theorem out of four given theorem can be used to prove two lines are parallel

Lets check first what each theorem says.

A ) Same-side exterior angle theorem says that when a transversal line intersects two parallel lines , same side exterior angles are supplementary. So first condition to apply is that two lines should be parallel and this first condition is used to say same side exterior angles are supplementary. So cannot use Same-side exterior angle theorem   to prove two lines are parallel.

B)  Converse of the alternate interior angles theorem : this theorem says when two lines intersected by transversal forms equal alternate interior angles then two lines are parallel. So yes this can use to check or prove that l and m are parallel by drawing a transversal intersecting l and m and checking alternate interior angles.

C ) Converse of the same-side interior angles theorem: this theorem says when two lines intersected by transversal forms supplementary same side interior angles then two lines are parallel. So yes this can use to check or prove that l and m are parallel by drawing a transversal intersecting l and m and checking same side interior angles.

D) Converse of corresponding angles postulate: this postulate says when two lines intersected by transversal forms congruent corresponding angles then two lines are parallel. So yes this can use to check or prove that l and m are parallel by drawing a transversal intersecting l and m and checking corresponding angles.

Hence out of four given options following three options are used to prove line l and m are parallel.

B) Converse of the alternate interior angles theorem  

C) Converse of the same-side interior angles theorem  

D) Converse of corresponding angles postulate

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