Question

In ABC shown below, BD/BA = BE/BC

B


D. E


A. C
The following flowchart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side BD BE BA BC = Given 4B 4B Reflexive Property of Equality 2. O1. AABC - ABED 2. Side-Angle-Side Similarity Postulate Which reason can be used to fill in the numbered blank space? O1 LABC - ABED 2. Side-Side-Side Similarity Theorem O1. LABC - ADBE 2 Side-Angle-Side Similarity Postulate 4BDE = 4BAC Corresponding Parts of Similar Triangles O1.AABC - ADBE 2. Side-Side-Side Similarity Theorem DE || AC Converse of the Corresponding Angles Postulate​

Answer 1

The proof uses the Side-Angle-Side Similarity Postulate to show similarity between triangles, the Corresponding Parts of Similar Triangles to establish equal angles, and the Converse of the Corresponding Angles Postulate to prove parallel lines.

In the flowchart proof provided, the missing statement and reason to fill in the numbered blank space are as follows:

Statement: Triangle ABC is similar to triangle ADBE.

Reason: Side-Angle-Side Similarity Postulate

Statement: Triangle ABC is similar to triangle ADBE.

Reason: Side-Angle-Side Similarity Postulate

Statement: Angle BDE is equal to angle BAC (Corresponding angles of similar triangles).

Reason: Corresponding Parts of Similar Triangles

Statement: BD/BA = BE/BC (Given).

Reason: Given

Statement: DE is parallel to AC (Converse of the Corresponding Angles Postulate).

Reason: Converse of the Corresponding Angles Postulate

The flowchart proof starts with the given proportionality relationship BD/BA = BE/BC and applies the Side-Angle-Side Similarity Postulate to establish the similarity of triangles ABC and ADBE. Then, it uses the Corresponding Parts of Similar Triangles to show that the corresponding angles are equal. Finally, the Converse of the Corresponding Angles Postulate is applied to conclude that DE is parallel to AC.

This proof demonstrates that when a line intersects two sides of a triangle and divides them proportionally, the line is parallel to the third side.

The question probable may be:

What is the step-by-step flowchart proof for establishing that if a line intersects two sides of a triangle and divides them proportionally, then the line is parallel to the third side?