Question

Select the correct answer from each drop-down menu. А D F B f G С In the diagram, ZADE & ZABC. The ratios and are equal. Reset Next FB : GC AE: EC

Answer 1

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,

`\angle A+\angle ADE+\angle AED=\angle A+\angle ABC+\angle ACB\Rightarrow\angle AED=\angle ACB`

Therefore, by the AAA criteria, the triangles ADE and ABC are similar.

Then the sides of the triangle are proportional,

`(AD)/(DB)=(AE)/(EC)`

This can also be written as,

`AD\colon DB=AE\colon EC`

This is the required answer.