Question

in $\triangle abc$ shown below, $\overline{de}$ is parallel to $\overline{ac}$.

the following two - column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

statement	reason
2. $\overline{ab}$ is a transversal that intersects two parallel lines.	2. conclusion from statement 1.
3.	3.
4. $\angle b \cong \angle b$	4. reflexive property of equality
5.	5.
6. $\frac{bd}{ba}=\frac{be}{bc}$	6. converse of the side - side - side similarity theorem

which statement and reason accurately completes the proof? (2 points)

$\bigcirc$ 3. $\angle bde \cong \angle bac$; corresponding angles postulate

1. $\triangle bde \sim \triangle bac$; angle - angle (aa) similarity postulate

$\bigcirc$ 3. $\triangle bde \sim \triangle bac$; corresponding angles postulate

Explanation:

Step1: Analyze the parallel lines and transversal

Since \( \overline{DE}\parallel\overline{AC}\) and \( \overline{AB}\) is a transversal, by the Corresponding Angles Postulate, \( \angle BDE\cong\angle BAC\).

Step2: Check for similarity of triangles

We have \( \angle B\cong\angle B\) (Reflexive Property of Equality) and \( \angle BDE\cong\angle BAC\). By the Angle - Angle (AA) Similarity Postulate, \( \triangle BDE\sim\triangle BAC\).

Answer:

1. \( \angle BDE\cong\angle BAC\); Corresponding Angles Postulate
2. \( \triangle BDE\sim\triangle BAC\); Angle - Angle (AA) Similarity Postulate