Question

In the given figure,ABC is a triangle, D and E are the points on BC such that ∆ADC ~∆AEB, then AD/AE is always equal to

Answer 1

In similar triangles, corresponding sides are all in the same proportion.

Here, ΔADC is similar to ΔAEB.

The corresponding side of AD is AE. Similarly, DC is EB and AC is AB.

So, their corresponding sides must also be proportional.

We have,

$\frac{AD}{AE} = \frac{AC}{AB} = \frac{DC}{EB}$

Here all the other options except (2) are showing the proportionality of different sides that don't always hold.

So, the answer is

(2) $\frac{AC}{AB}$

Answer 2

In the triangle ADE

AD = AE (this is given)

∠AED = ∠ADE (these are equal)

= 180 - ∠AED  

= 180 - ∠ADE

∠AEC = ∠ADB (this is equation 1)

In Δ ABD and ΔACE

AD  = AE (given)

∠ADB = ∠AEC

ΔABD is congruent to ΔACE

AB = AC

If there is any confusion please leave a comment below.