The missing reason is the Converse alternate interior angles theorem.
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
In the image, you can observe a diagram representing this problem.
We know by given that g||h and ∠2 ≅ ∠3
From the parallelism between line g and line h, we deduct several congruences between angles.
∠2≅∠1, by corresponding angles (same side of the transversal, one interior, the other exterior to parallels).
Now, to demonstrate,e || f we must demonstrate congruence between angle 2 and an angle on the intersection between line g and line f.
In the parallelogram formed, we know
∠2+∠3+180-∠1=360
Where x is the angle at the intersection of line g and line f.
But, we know ∠2≅∠3 and,∠2≅∠1 so
∠2+∠2+180-∠2+x =360
∠2 + x =180
Notice that we don't have a congruence, however, there's a theorem that states that the same-side interior angles of parallels are supplementary.
In this case, we use the corollary of that theorem, which states if two same-side interior angles are supplementary, then the lines are parallels.
e || f
However, according to the choices of the problem, the missing proof is the "converse alternate interior angles theorem", because the problem was demonstrated using transitive property, to show that angles 1 and 3 are congruent, thereby converse alternate interior angles theorem, lines e and f are parallels.
To know more about Trigonometry follow
https://brainly.com/question/24349828
#SPJ1
