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In the given figure, D and E are points ...

In the given figure, D and E are points on the side BC of a `DeltaABC` such that BD = CE and AD = AE. Show that `DeltaABD~=DeltaACE.`

Text Solution

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GIVEN A `DeltaABC" in which "D and E` are points on BC such that BD = CE and AD = AE.
TO PROVE `DeltaABD~=DeltaACE.`
PROOF We know that the angles opposite to equal sides of a triangle are equal.
So, in `DeltaADE`, we have
`AD=AE rArr angleADE=angleAED`
`rArr" "180^(@)-angleADE=180^(@)-angleAED`
`rArr" "angleADB=angleAEC." ...(i)"`
Now, in `DeltaABD and DeltaACE`, we have
`AD = AE" (given)"`
`angleADB=angleAEC" [proved in (i)]"`
`BD=CE" (given)"`
`therefore" "DeltaABD~=DeltaACE." (SAS-criteria)."`
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