Question

In below figure, ∠A = ∠CED, Prove that ΔCAB ~ ΔCED. Also, find the value of x.

Answer 1

We have, ∠A = ∠CED

In ΔCAB and ΔCED

∠C = ∠C                               [Common]

∠A = ∠CED                             [Given]

Then, ΔCAB ~ ΔCED                  [By AA similarity]

`therefore"CA"/"CE"="AB"/"ED"`                 [Corresponding parts of similar Δ are proportional]

`rArr15/10=9/x`

`rArrx=(10xx9)/15=90/15=6 ` cm