Question

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

I. OCJA
II. ODAL
III. CODNZAJL
IV. DCOZJAL
A) I and III
B) I, III, and IV
C) II only
D) III only

Answer 1

If AOCD ~ AJAL, the ratios of the corresponding sides of the triangles are equal.

Step-by-step explanation:

If AOCD ~ AJAL, then the corresponding sides of the triangles are proportional. This means that the ratios of the corresponding sides are equal. In this case, the ratios would be:

• AD/AJ = AO/AO = AO/OD
• OC/OA = OJ/OA = OJ/OC
• CD/JL = AO/AJ = AO/AL

Based on these ratios, we can determine the following:

1. Statement I: True. The ratios of AD to AJ, OC to OA, and CD to JL are all equal.
2. Statement II: False. The ratio of OC to OJ is not equal to the ratio of OA to OA.
3. Statement III: True. The ratios of AO to OD, OJ to OA, and AO to AL are all equal.
4. Statement IV: False. The ratio of CD to JL is not equal to the ratio of AD to AJ.