question 2 of 2 select the correct answer from each drop - down menu. complete the sentences to distinguish between a conjecture, a postulate, and a theorem. postulates and conjectures are similar in that they both have not been proven true. postulates are statements that are taken to be true without requiring proof. drop - down menu options: postulates, conjectures, theorems another drop - down menu: not been, have been another drop - down menu: proven true, etc. (partially visible) reset

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# Brief Explanations:
1. First blank: Conjectures are statements that have not been proven true (they are proposed as true but need proof). Postulates and theorems have different proof statuses, so "Conjectures" fit here.
2. Second blank: Conjectures "have not been" proven (they are unproven, while postulates are taken as true without proof yet not conjectures, and theorems are proven).
3. Third blank: Theorems "have been proven" using rigorous logic (theorems are statements proven from postulates, definitions, etc.). Wait, no, re - examining: The sentence structure is "Postulates and conjectures are similar in that they both have [blank1] [blank2] proven true. [blank3] are statements that are taken to be true without requiring proof." Wait, maybe I misread. Let's re - analyze:

The first part: "Postulates and conjectures are similar in that they both have [not been] proven true." Because postulates are assumed true (not proven), conjectures are unproven (proposed, need proof). Then "Postulates are statements that are taken to be true without requiring proof." Wait, no, the third blank: the options are Postulates, Conjectures, Theorems. The definition of postulates is statements taken as true without proof. Theorems are proven. Conjectures are unproven. So:

1. First blank (the subject of "have not been proven"): Conjectures (since conjectures are unproven, postulates are assumed true without proof (not proven in the sense of needing proof), but the similarity is they are not proven. Wait, the first sentence: "Postulates and conjectures are similar in that they both have [not been] proven true." So the first blank (the noun) is "Conjectures"? Wait, no, the first drop - down has Postulates, Conjectures, Theorems. Let's structure the sentence: "Postulates and conjectures are similar in that they both have [Conjectures? No, the first blank is the noun. Wait, the sentence is "Postulates and conjectures are similar in that they both have [blank1] [blank2] proven true." Wait, maybe the first blank is "Conjectures" (no, postulates and conjectures: postulates are assumed true (not proven), conjectures are unproven. So the similarity is they "have not been" proven. Wait, the second blank is "not been" (from the options). Then the first blank: the subject. Wait, maybe the first blank is "Conjectures" (no, the sentence is about postulates and conjectures. Wait, let's look at the options for the first blank: Postulates, Conjectures, Theorems.

Let's re - express the sentences:

1. "Postulates and conjectures are similar in that they both have [Conjectures? No, that doesn't make sense. Wait, maybe the first blank is "Conjectures" (no, the sentence is comparing postulates and conjectures. So the first blank: the thing that has not been proven. Conjectures are unproven, postulates are assumed true (not proven in the sense of a logical proof). So "Postulates and conjectures are similar in that they both have [not been] proven true." Wait, the first blank is the noun: "Conjectures" (no, the structure is "they both have [noun] [not been] proven true"? No, maybe the first blank is "Conjectures" (the subject) and the second blank is "not been". Then "Postulates and conjectures are similar in that they both have Conjectures not been proven true"? No, that's wrong.

Wait, maybe the correct breakdown is:

- First blank: Conjectures (because conjectures are unproven, postulates are assumed true (not proven), so their similarity is they are not proven. So "Postulates and conjectures are similar in that they both have Conjectures? No, I think I messed up. Let's use the options:

First drop - down: Conjectures (because conjectures are unproven, postulates are assumed true (not proven), so the similarity is they are not proven. So the first blank: Conjectures (no, the subject is postulates and conjectures. Wait, the first blank is the noun that has not been proven. So "Postulates and conjectures are similar in that they both have [Conjectures] [not been] proven true." No, that's incorrect. Wait, maybe the first blank is "Postulates" no. Wait, let's check the definitions:

- Conjecture: a statement that is proposed as true, but not yet proven.

- Postulate: a statement that is assumed to be true without proof (used as a basis for reasoning).

- Theorem: a statement that has been proven true using logic, postulates, definitions, etc.

So:

1. "Postulates and conjectures are similar in that they both have [not been] proven true." Wait, the second blank is "not been". Then the first blank (the noun) is "Conjectures"? No, the sentence is "Postulates and conjectures are similar in that they both have [Conjectures] [not been] proven true." No, that's wrong. Wait, maybe the first blank is "Conjectures" (the subject) and the second blank is "not been", and the third blank is "Postulates".

Let's build the sentences:

- "Postulates and conjectures are similar in that they both have Conjectures not been proven true." No, that's not right. Wait, maybe the first blank is "Conjectures" (the thing that is unproven), the second blank is "not been", and the third blank is "Postulates".

So:

1. First blank: Conjectures

2. Second blank: not been

3. Third blank: Postulates

Because:

- Postulates and conjectures are similar in that Conjectures (wait, no, postulates and conjectures: both postulates and conjectures have not been proven true. Postulates are assumed true without proof (so not proven), conjectures are unproven. Then "Postulates are statements that are taken to be true without requiring proof."

Yes, that makes sense.

# Answer:
1. First blank: Conjectures
2. Second blank: not been
3. Third blank: Postulates

(If the options for the blanks are as follows: first drop - down: Conjectures; second drop - down: not been; third drop - down: Postulates)

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