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Which shows two triangles that are congruent by the SSS congruence theorem? Triangles A B C and D E C are connected at point C. Angles A B C and C E D are right angles. The lengths of sides A B and E D are congruent. Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent. Triangles A B C and D E C are connected at point C. The lengths of sides A C and C E are congruent. Angles B A C and C E D are congruent. Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.

The last case shows that the two triangles are congruent by SSS congruency theorem

Step-by-step explanation:

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.

With this case.  You have sides  AB = AD,  BC = DC,  and then can conclude that AC= AC by reflexive property  because AC is the common side.

so triangle ABC = triangle ADC  by SSS congruency

CASE 1.) Triangles A B C and D E C are connected at point C. Angles A B C and C E D are right angles. The lengths of sides A B and E D are congruent.   You would only know  one pair of sides and one pair of angles that are congruent.

CASE 2.)  Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent.  You would only know 2 pairs of congruent sides.  

CASE 3.)Triangles A B C and D E C are connected at point C. The lengths of sides A C and C E are congruent. Angles B A C and C E D are congruent.   You would  only know a pair of angles and a pair of sides.  Not enough for congruency.

CASE 4.) Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.

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step-by-step explanation: