Question

19
select the correct answer from each drop - down menu.
points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of △abc is 180°

statement	reason
points a, b, and c form a triangle	given
let $overline{de}$ be a line passing through b and parallel to $overline{ac}$	definition of parallel lines

Explanation:

Step1: Recall angle - related properties

We know that when a transversal intersects two parallel lines, alternate - interior angles are equal. Since $DE\parallel AC$, $\angle 1=\angle 4$ (alternate - interior angles) and $\angle 3=\angle 5$ (alternate - interior angles).

Step2: Consider the straight - line angle

The sum of angles on a straight line is $180^{\circ}$. So, $\angle 4+\angle 2+\angle 5 = 180^{\circ}$.

Step3: Substitute the equal angles

Substituting $\angle 1$ for $\angle 4$ and $\angle 3$ for $\angle 5$ in the equation $\angle 4+\angle 2+\angle 5 = 180^{\circ}$, we get $\angle 1+\angle 2+\angle 3 = 180^{\circ}$, which is the sum of the interior angles of $\triangle ABC$.

Answer:

The sum of the interior angles of $\triangle ABC$ is $180^{\circ}$ because of the properties of parallel lines (alternate - interior angles) and the fact that the sum of angles on a straight line is $180^{\circ}$.