Without solving for "x", which criteria can be used to prove the triangles congruent? justify.

a) without solving for "x", the triangles cannot be proven congruent.
c) asa; right angles cad and ceb are congruent; ac≅ ec; vertical angles acd and ecb are congruent;
d) aas; right angles cad and ceb are congruent; ac≅ ec; vertical angles acd and ecb are congruent;

Two triangles are congruent if their corresponding sides have the same length and their corresponding angles have the same measurement.
 One of the cases that proves the congruence of triangles is the case:
 Angle-Side-Angle
 Two triangles are congruent if they have equal two of their respective angles and the side between them.
 Answer
 C) ASA; right angles CAD and CEB are congruent; AC≅ EC; vertical angles ACD and ECB are congruent;

the value of the diversity index D is Zero (0)

Step-by-step explanation:

Just as the meaning of diversity index is boldly explained in the question, it is the probability that randomly selected organism from a population are from a different species.

Now if the organisms are all from the same species in a population  then it is impossible to select two organisms from different species.

That is, we can never select two organisms that are not from the same species.

Hence, we cant fulfil or meet the definition of diversity index .

Therefore in this situation the value of our diversity index D will be exactly zero, D = 0.