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Consider the following statements of congruence: Given triangle ABC and segment DE such that AB is congruent to DE. Then on a given side of DE there...

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Consider the following statements of congruence: 1. Given triangle ABC and segment DE such that AB is congruent to DE. Then on a given side of DE there is a unique point F such that AC is congruent to DF and BC is congruent to EF. 2. Given triangles ADC and A’D’C’ and given A*B*C and A’*B’*C’. If AB is congruent to A’B’, BC is congruent to B’C’ and AD is congruent to A’D’, and BD is congruent to B’D’, then CD is congruent to C’D’. (rigidity of a triangle with a tail, figure below) Prove there statements.
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