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Use the information marked to prove : ...

Use the information marked to prove :
(i) `DeltaEAC cong DeltaDBC` (ii) `EC = DC`
Also state the Euclid's axiom used in proving the congruency of two triangles.

Text Solution

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(i) We have `angle3=angle4` (given)
`implies angle3+angle5=angle4+angle5`
(adding same angle on both sides)
This is the second axiom of Euclid : If equals are added to equals, the wholes are equal.
`implies angleACE=angleBCD`
Now, in `DeltaEAC` and `DeltaDBC`,
`:. {(angleACE=angleBCD,"(just proved)"),(AC=BC,"(given)"),(angleEAC=angleCBD,"(given)"):}`
`:. DeltaEAC cong DeltaDBC` (ASA) Hence Proved.
(ii) Therefore, `EC=DC` (by c.p.c.t) Hence Proved.
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