Question

please solve this question​

Answer 1

AD and CE are altitudes, which intersect each other at P.

(i) In ∆AEP and ∆CDP

∠AEP = ∠CDP = 90° [given]

and    ∠APE = ∠CPD

[vertically opposite angles]

Therefore, by using AA similar condition

∆AEP ~ ∆CDP.

(ii) In ∆ABD and ∆CBE

∠ADB = ∠CEB = 90° [given]

and    ∠B = ∠B    [common]

Therefore, by using AA similar condition

∆ABD ~ ∆CBE.

(iii)    In ∆AEP and ∆ADB

∠AEP = ∠ADB = 90° [given]

and    ∠PAE = ∠DAB [common]

Therefore, by using AA similar condition

∆AEP ~ ∆ADB

(iv)    In ∆PDC and ∆BEC

∠PDC = ∠CEB = 90° [given]

∠PCD = ∠ECB [common]

Therefore, by using AA similar condition

∆PDC ~ ∆BEC.