1.

InFigure altitudes AD and CE of DABCintersect each other at the point P. Show that:(i) `DeltaA E P DeltaC D P`(ii) `DeltaA B D DeltaC B E`(iii) `DeltaA E P DeltaA D B`(iv) `DeltaP D C DeltaB E C`

Answer» In `Delta AEP and Delta CDP`, we have
`angle AEP= angle CDP` [ eacjh equal to `90^(@)`]
`angle APE= angle CPD` [ verticapply opposite `angle`]
`:. Delta AEP ~ Delta CDP` [ by AA- similarity]
(ii) In `Delta ABD and Delta CBE`, we have
`angle ADB= angle CEB=90^(@)`
`angle B= angle B` [ common]
`:. Delta ABD~ Delta CBE` [ by AA- similarity]
(iii) In `Delta AEP and Delta ADB`, we have
`angle AEP=angleADB=90^(@)`
`angle EAP= angle DAB` ( common)
Hence, `Delta AEP~ Delta ADB` [ by AA- similarity]
(iv) In `Delta PDC and Delta BEC`, we have
`angle PDC= angle BEC= 90^(@)`
`angle PCD= angle BCE` (common)
`:.Delta PDC ~ Delta BEC` [ by AA- similarity]


Discussion

No Comment Found

Related InterviewSolutions