Answer:
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
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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.
