Question

Daniel wants to prove that the interior angles of any triangle sum to 180°. He draws a line through one vertex parallel to the opposite side, and then he labels all the angles formed.
Drag a reason to match each statement in Daniel's proof in the table below.

Answer 1

Alternate interior angles theorem.

Step-by-step explanation:

By using the definition of Alternate Interior Angles theorem, we can say that If a transversal cuts any two parallel lines, then those pairs of alternate interior angles are seems to be  congruent.

So in the given triangle,

∠4 ≅ ∠2

∠5 ≅ ∠3

Sum of all the angles in a triangle = 180°

∠1 + ∠2 + ∠3 = 180°

Since from the above congruence, we can write that

∠1 + ∠4 + ∠5 = 180°

Hence proved.