Question

1) In AABC AD & CE are the altitudes intersect each other at the point P. Show that
a) AAEP- ACDP, b) AABD - ACBE, C) AAEP - AADB d) APDC - ABEC
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Answer 1

Step-by-step explanation:

In △AEP and △CDP,

∠APE=∠CPD (Vertically opposite angle)

∠AEP=∠CDP=90

o

∴ By AA criterion of similarity, △AEP ∼ △CDP

In △ABD and △CBE

∠ADB=∠CEB=90

o

∠B is common

∴ By AA criterion of similarity, △ABD ∼ △CBE

In △AEP and △ADB

∠AEP=∠ADB=90

o

∠A is common

∴ By AA criterion of similarity, △AEP ∼ △ADB

△PDC and △BEC

∠PDC=∠BEC=90

o

∠C is common

∴ By AA criterion of similarity, △PDC ∼ △BEC