Triangle abc is shown below.
triangle abc; line passes through points d, b, and e
given: ∆abc
prove: all three angles of ∆abc add up to 180°.
the flow chart with missing reason proves the measures of the interior angles of ∆abc total 180°.
which reason can be used to fill in the numbered blank space?
associative property of addition
triangle exterior angle theorem
angle addition postulate
commutative property of addition

The correct answer (though it is not one of the choices) is:

Alternate Interior Angles Theorem.

Explanation:

Alternate interior angles are angles that are inside the parallel lines and on opposite sides of the transversal.  Treating BA as a transversal, ∠DBA and ∠BAC are both inside the parallel lines and on opposite sides of BA, the transversal.  This makes them alternate interior angles, and means that they are congruent.

any options?

step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc