Answer:
Step-by-step explanation:
Given: DE║BC
To prove: [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex]
Statements Reasons
1). DE║BC 1). Given
2). ∠1 ≅ ∠4, ∠3 ≅ ∠4 2). Corresponding angles theorem
3). ΔADE ~ ΔABC 3). AA Similarity theorem
4). [tex]\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}[/tex] 4). Corresponding sides are proportional
5). [tex]\frac{\text{AD+DB}}{\text{AD}}=\frac{\text{AE+EC}}{AE}[/tex] 5). Segment addition postulate
6). [tex]1+\frac{\text{DB}}{\text{AD}}=1+\frac{\text{EC}}{\text{AE}}[/tex] 6). [tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]
7). [tex]\frac{\text{DB}}{\text{AD}}=\frac{\text{EC}}{\text{AE}}[/tex] 7). Subtract 1 from both sides
8). [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex] 8). Take the reciprocal of both sides
