Question

In the given triangle DE II BC, which of the following statements is true?

• A. $\frac{AD}{AB}=\frac{DE}{BC}$
• B. $\frac{AB}{AB}=\frac{DE}{BC}$
• C. $\frac{AD}{AB}=\frac{DB}{BC}$
• D. $\frac{AB}{AB}=\frac{DC}{BC}$

Answer 1

The correct option is A

$\frac{AD}{AB}=\frac{DE}{BC}$

Consider $△ADE$ and $△ABC$

$\angle DAE$ and $\angle BAC$ are common.

$\angle ADE=\angle$ABC

Thus the 2 triangles are similar triangles by AA similarity.

The corresponding sides of these 2 triangles are proportional.

$\frac{AD}{AB}=\frac{DE}{BC}$