Akira gave a problem to her sister Kiara. However, Kiara got stuck. Help Kiara identify whether the triangles are congruent and choose the correct option.
Yes, △ABC ≅△DCE
No, they are not congruent
Yes, △DCE ≅△BAC
Yes, △DCE ≅△CAB
A
No, they are not congruent
B
Yes, △DCE ≅△BAC
C
Yes, △DCE ≅△CAB
D
Yes, △ABC ≅△DCE
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Solution
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In the given figure, MD=MC=EC=EB=AB
⇒DC=MD+MC=CE+EB=CB ... ( 1 )
⇒Also, AB=EC ...( 2 )
⇒In △DEC and △CAB
⇒DE=CA [given]
⇒DC=CB [from ( 1 ) ]
⇒EC=AB [Given ]
∴△DEC≅△CAB [By SSS criteria ]
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