Question

If AOCD = AJAL, then which of the following statements are true?

I. OCJA
II. ODSAL
III. COD = ZAJL
IV. DCOZJAL
a) I and III
b) II and IV
c) I, II, and III
d) III and IV

Answer 1

In mathematics, when given a scenario with congruent angles represented by different letters, we can determine the true statements involving the angles.

Step-by-step explanation:

To determine which of the statements are true when AOCD = AJAL, we need to examine the relationship between the given letters and their corresponding angles. In this case, the letter pairs are associated with angles in the same way. For example, OA represents angle O, OC represents angle C, and so on.

Let's analyze each statement:

1. OCJA: This statement is true. The angles represented by the letters in OCJA (OC, CJ, and AJ) are indeed the same in the given scenario.
2. ODSAL: This statement is false. The letters D and S do not have corresponding letters in the other pair, so the angles represented by those letters cannot be equal.
3. COD = ZAJL: This statement is false. While COD and ZAJL are both expressions involving the same letters, they do not represent the same angles.
4. DCOZJAL: This statement is false. It is not clear what this expression represents, but it is not equal to AOCD or AJAL.

Therefore, the correct answer is (a) I and III.