In triangle A B C\ a n d\ C D E , if A C...

In triangle `A B C\ a n d\ C D E ,` if `A C=C E ,\ B C=C D ,\ /_A=60^0,\ /_C=30^0\ a n d\ /_D=90^0dot` Are two triangle congruent?

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Solution
Yes, these two triangles congruent.
Given,
`AC = CE`
`BC = CD`
`/_A= 60@`
`/_C= 30@`
`/_D=90@`
Consider the attached figure, while going through the following steps.
In `/_\ABC` and `/_\CDE`
`AC = EC`
`BC = CD`
`/_BAC = /_CED`
Therefore both the triangles are congruent considering 'SAS' criteria.

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