Question

In triangle ABC, DE is parallel to BC; where D and E are the points on AB and AC respectively.
Prove: ∆ADE ~ ∆ABC.
Also, find the length of DE, if AD = 12 cm, BD = 24 cm BC = 8 cm.

Answer 1

In ∆ ADE and ∆ ABC, DE is parallel to BC, so corresponding angles are equal.

`∠ADE=∠ABC`

`∠AED=∠ACB`

Hence, ∆ADE ~ ∆ABC (By AA similarity criterion)
`∴(AD)/(AB)=(DE)/(BC)`

`12/(12+24)=(DE)/8`

`DE=12/36xx8=8/3`

Hence DE = `8/3`