Question

Prove the Triangle Proportinality Theorem

Answer 1

Explanation:

Given: DE║BC

To prove:
`\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}`

Statements Reasons

1). DE║BC 1). Given

2). ∠1 ≅ ∠4, ∠3 ≅ ∠4 2). Corresponding angles theorem

3). ΔADE ~ ΔABC 3). AA Similarity theorem

4).
`\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}` 4). Corresponding sides are proportional

5).
`\frac{\text{AD+DB}}{\text{AD}}=\frac{\text{AE+EC}}{AE}` 5). Segment addition postulate

6).
`1+\frac{\text{DB}}{\text{AD}}=1+\frac{\text{EC}}{\text{AE}}` 6).
`(a+b)/(c)=(a)/(c)+(b)/(c)`

7).
`\frac{\text{DB}}{\text{AD}}=\frac{\text{EC}}{\text{AE}}` 7). Subtract 1 from both sides

8).
`\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}` 8). Take the reciprocal of both sides