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Sagot :
Consider the given figure, in the triangle ADE and ABC,
Angle A is common in both the triangles.
Already given that angle ADE is equal to angle ABC.
Consider the property that the sum of all three angles of a triangle is 180 degree,
[tex]\angle A+\angle ADE+\angle AED=\angle A+\angle ABC+\angle ACB\Rightarrow\angle AED=\angle ACB[/tex]Therefore, by the AAA criteria, the triangles ADE and ABC are similar.
Then the sides of the triangle are proportional,
[tex]\frac{AD}{DB}=\frac{AE}{EC}[/tex]This can also be written as,
[tex]AD\colon DB=AE\colon EC[/tex]This is the required answer.
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