Question

Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB

Answer 1

Explanation:

Given:

AB║DC and BC║AE

To prove:

`\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}`

Statements Reasons

1). ∠ABE ≅ ∠CDB 1). Alternate interior angles

2). ∠AEB ≅ ∠CBD 2). Alternate interior angles

3). ΔCBD ~ ΔAEB 3). AA property of similarity

4).
`\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}` 4). Property of similarity [Corresponding sides of two similar triangles are proportional]