In figure ,D and E are Points on side BC of a `Delta ABC` such that BD – InterviewSolution

InterviewSolution

1.	In figure ,D and E are Points on side BC of a `Delta ABC` such that BD=CE and AD=AE.Show that `Delta ABD cong Delta ACE.`
Answer» Given D and E are the point on side BC of a `Delta ABC `Such that BD =CE and AD=AE. To show `Delta ABD cong Delta ACE` Proof We have,`" " AD=AE " "[given]` `rArr " "angleADE=angleAED " "…(i)` `" "["since angle opposite to equal sides are equal "]` We have `" "angleADB+angleADE=180 ^(@) " " ["linear Pair axiom"] ` `rArr " "angleADB=180^(@)-angleAED` `" "=180^(@)-angleAED " " ["from Eq.(i)"]` `In Delta ABD and Delta ACE,` `" "angleADB=angleAEC " "[because angleAEC + angleAED=180^(@),"Linear Pair axiom"]` `" "BD=CE " "["given"]` `therefore " "DeltaABD cong Delta ACE " "["by SAS congruence rule"]`

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