Prove hint first prove existence then prove uniquenessSoluti

Prove

(hint, first prove existence, then prove uniqueness)

Given that AB =DE

Consider cutting the triangle ABC from the plane and pasting so that AB lies along DE with A on E

Since AB =DE, B coincindes with E.

Now we have the vertex C not pasted.

C can be pasted either on the top of DE or at the bottom of DE

Let the vertex new be named as F

Now we have ABC congruent to DEF and DEF (Bottom)

Hence proved.

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Uniqueness: Let DEF congruent to ABC.

If possible let there be two triangles DEF and DEF\' lying on the same side of DE and congruent to ABC.

Then BC = EF and also BC = EF\' by CPCT property

Also angle ABC = Angle DEF = Angle DEF\'

This is possible for the same side of DE if and only if F coincides with F\'

Thus uniqueness is proved