Question

Triangle Proportionality Theorum How does one find the ratio?

I need to fill in the blanks but I'm not sure what the correct answer is
using the picture:
(upper left)/(whole left) = (upper parallel)/ ?

Answer 1

`color(green)((BC) / (DE) = (AC) / (AE) = (AB) / (AD)`

Explanation:

Consider Triangles ABC & ADE

`hatA` is common

`hatB = hat D`, `hatC = hatE`

Since all the three angles of one triangle equal to the other, both the triangles are similar.

THEN THEIR CORRESPONDING SIDES ARE IN THE SAME PROPORTION

Side corresponding to each angle is as under :

In triangle ABC : `hatA -> BC, hat B -> CA, hatC -> AB`

In triangle ADE `hatA -> DE, hatD -> AE, hatE -> AD`

Therefore, `color(green)((BC) / (DE) = (AC) / (AE) = (AB) / (AD)`