Title: conjecture/compound statement
Course: quiz duplicate error

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- A right angle measures 90º or an isosceles triangle has two congruent sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. The symbol for logical and is [Image].)
- A right angle measures 90º and an isosceles triangle has two congruent sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. The symbol for logical and is [Image].)
- A right angle measures 90º and an isosceles triangle does not have two congruent sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. The symbol for logical and is [Image].)
- A right angle measures 90º or an isosceles triangle does not have two congruent sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. The symbol for logical and is [Image].)
A: A right angle measures 90º and an isosceles triangle has two congruent sides. True

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

s or q
- A decagon has 12 sides or a right angle measures 90º. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A decagon has 12 sides or a right angle measures 90º. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A decagon has 12 sides and a right angle measures 90º. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A decagon has 12 sides and a right angle measures 90º. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
A: A decagon has 12 sides or a right angle measures 90º. True

Q: Make a conjecture about the next item in the sequence.

[Image]
- 1024 (Start with 1. Add, subtract, or multiply the same number to each number to get the next one.)
- 1025 (Start with 1. Add, subtract, or multiply the same number to each number to get the next one.)
- 4096 (Start with 1. Add, subtract, or multiply the same number to each number to get the next one.)
- 1022 (Start with 1. Add, subtract, or multiply the same number to each number to get the next one.)
A: 1024

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: [Image] is supplementary to [Image] and [Image] is supplementary to [Image].
Conjecture: [Image] is supplementary to [Image].
- False; they could be right angles. (If two angles are supplementary their measures total 180. [Image] could only be supplementary to [Image] if they are both right angles.)
- False; they could be congruent angles. (If two angles are supplementary their measures total 180. [Image] could only be supplementary to [Image] if they are both right angles.)
- True (If two angles are supplementary their measures total 180. [Image] could only be supplementary to [Image] if they are both right angles.)
- False; they could be vertical angles. (If two angles are supplementary their measures total 180. [Image] could only be supplementary to [Image] if they are both right angles.)
A: False; they could be congruent angles.

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: [Image]
Conjecture: [Image]
- False; [Image]. (Because m is squared in the example, m could be positive or negative.)
- True (Because m is squared in the example, m could be positive or negative.)
- False; [Image]. (Because m is squared in the example, m could be positive or negative.)
- False; [Image]. (Because m is squared in the example, m could be positive or negative.)
A: False; [Image].

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- A decagon has 12 sides and an isosceles triangle has two congruent sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A decagon has 12 sides and an isosceles triangle has two congruent sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A decagon has 12 sides or an isosceles triangle has two congruent sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A decagon has 12 sides or an isosceles triangle has two congruent sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
A: A decagon has 12 sides or an isosceles triangle has two congruent sides. True

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: Two angles are supplementary.
Conjecture: They are both acute angles.
- False; either both are right or they are adjacent. (If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the other acute.)
- True (If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the other acute.)
- False; either both are right or one is obtuse. (If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the other acute.)
- False; they must be vertical angles. (If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the other acute.)
A: False; either both are right or one is obtuse.

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- An isosceles triangle has two congruent sides and a right angle measures 90º. True (Two or more statements can be joined to form a compound statement. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical or is [Image].)
- An isosceles triangle has two congruent sides or a right angle measures 90º. True (Two or more statements can be joined to form a compound statement. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical or is [Image].)
- An isosceles triangle has two congruent sides or four points are always coplanar. True (Two or more statements can be joined to form a compound statement. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical or is [Image].)
- An isosceles triangle has two congruent sides or a right angle measures 90º. False (Two or more statements can be joined to form a compound statement. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical or is [Image].)
A: An isosceles triangle has two congruent sides or a right angle measures 90º. True

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: points R, S, and T
Conjecture: R, S, and T are coplanar.
- False; the points do not have to be in a straight line. (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
- True (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
- False; the points to not have to form right angles. (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
- False; one point may not be between the other two. (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
A: True

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

q or r
- A right angle measures 90º and four points are always coplanar. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or.)
- A right angle measures 90º or a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or.)
- A right angle measures 90º or four points are always coplanar. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or.)
- A right angle measures 90º or four points are always coplanar. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or.)
A: A right angle measures 90º or four points are always coplanar. True

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: [Image] are coplanar.
Conjecture: They are vertical angles.
- False; the angles may be supplementary. (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
- True (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
- False; one angle may be in the interior of the other. (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
- False; the angles may be adjacent. (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
A: False; the angles may be supplementary. / False; one angle may be in the interior of the other. / False; the angles may be adjacent.

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: [Image] are coplanar.
Conjecture: They are vertical angles.
- False; the angles may be supplementary. (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
- True (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
- False; one angle may be in the interior of the other. (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
- False; the angles may be adjacent. (Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one.)
A: False; one angle may be in the interior of the other.

Q: Make a conjecture about the next item in the sequence.

[Image]
- [Image] (Start with 6. Do one operation to get the next number. Do a different operation to get the next number. Repeat.)
- [Image] (Start with 6. Do one operation to get the next number. Do a different operation to get the next number. Repeat.)
- [Image] (Start with 6. Do one operation to get the next number. Do a different operation to get the next number. Repeat.)
- [Image] (Start with 6. Do one operation to get the next number. Do a different operation to get the next number. Repeat.)
A: [Image]

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: [Image]
Conjecture: [Image]
- False; the angles are not vertical. (Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent.)
- True (Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent.)
- False; the angles are not complementary. (Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent.)
- False; there is no indication of the measures of the angles. (Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent.)
A: False; there is no indication of the measures of the angles.

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- A right angle measures 90º or four points are always coplanar, and a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A right angle measures 90º and four points are always coplanar, or a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A right angle measures 90º and four points are always coplanar, or a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- A right angle measures 90º or four points are always coplanar, and a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
A: A right angle measures 90º and four points are always coplanar, or a decagon has 12 sides. False

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: point B is in the interior of [Image].
Conjecture: [Image]
- False; [Image] may be obtuse. (Angles are congruent only if their measures are equal. Point B may be closer to line AD or line DC so the measures would not be equal.)
- True (Angles are congruent only if their measures are equal. Point B may be closer to line AD or line DC so the measures would not be equal.)
- False; just because it is in the interior does not mean it is on the bisecting line. (Angles are congruent only if their measures are equal. Point B may be closer to line AD or line DC so the measures would not be equal.)
- False; [Image]. (Angles are congruent only if their measures are equal. Point B may be closer to line AD or line DC so the measures would not be equal.)
A: False; just because it is in the interior does not mean it is on the bisecting line.

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar.
- False; the four points do not have to be in a straight line. (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
- True (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
- False; two points are always coplanar but four are not. (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
- False; three points are always coplanar but four are not. (Coplanar points always lie in the same plane. Three points are always coplanar but four are not.)
A: False; three points are always coplanar but four are not.

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- Four points are always coplanar, or a right angle measures 90º and a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- Four points are always coplanar, and a right angle measures 90º or a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- Four points are always coplanar, or a right angle measures 90º and a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- Four points are always coplanar, and a right angle measures 90º or a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
A: Four points are always coplanar, and a right angle measures 90º or a decagon has 12 sides. False

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

p and r
- An isosceles triangle has two congruent sides and four points are always coplanar. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and.)
- An isosceles triangle has two congruent sides and a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and.)
- An isosceles triangle has two congruent sides and four points are always coplanar. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and.)
- An isosceles triangle has two congruent sides and a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and.)
A: An isosceles triangle has two congruent sides and four points are always coplanar. False

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: segments RT and ST; twice the measure of [Image].
Conjecture: S is the midpoint of segment RT.
- True (Even though they have a common point, the two segments do not have to be on the same line.)
- False; point S may not be on [Image]. (Even though they have a common point, the two segments do not have to be on the same line.)
- False; lines do not have midpoints. (Even though they have a common point, the two segments do not have to be on the same line.)
- False; [Image] could be the segment bisector of [Image]. (Even though they have a common point, the two segments do not have to be on the same line.)
A: False; point S may not be on [Image].

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: a concave polygon
Conjecture: It can be regular or irregular.
- False; to be concave the angles cannot be congruent. (Concave polygons must be irregular. This means all sides and angles are not congruent.)
- True (Concave polygons must be irregular. This means all sides and angles are not congruent.)
- False; all concave polygons are regular. (Concave polygons must be irregular. This means all sides and angles are not congruent.)
- False; a concave polygon has an odd number of sides. (Concave polygons must be irregular. This means all sides and angles are not congruent.)
A: False; to be concave the angles cannot be congruent.

Q: Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
(Look up the definition of a regular polygon in the glossary. It will help you!)

Given: a concave polygon
Conjecture: It can be regular or irregular.
- False; to be concave the angles cannot be congruent. (Concave polygons must be irregular. This means all sides and angles are not congruent.)
- True (Concave polygons must be irregular. This means all sides and angles are not congruent.)
- False; all concave polygons are regular. (Concave polygons must be irregular. This means all sides and angles are not congruent.)
- False; a concave polygon has an odd number of sides. (Concave polygons must be irregular. This means all sides and angles are not congruent.)
A: False; to be concave the angles cannot be congruent.

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- An isosceles triangle has two congruent sides and a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- An isosceles triangle has two congruent sides or a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- An isosceles triangle has two congruent sides or a decagon has 12 sides. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- An isosceles triangle has two congruent sides and a decagon has 12 sides. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
A: An isosceles triangle has two congruent sides and a decagon has 12 sides. False

Q: Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.
q: A right angle measures 90º
r: Four points are always coplanar.
s: A decagon has 12 sides.

[Image]
- Four points are always coplanar and a right angle measures 90º. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- Four points are always coplanar and a right angle measures 90º. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- Four points are always coplanar or a right angle measures 90º. False (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
- Four points are always coplanar or a right angle measures 90º. True (Two or more statements can be joined to form a compound statement. A conjunction is a compound statement formed by joining two or more statements with the word and. A disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is [Image]. The symbol for logical or is [Image].)
A: Four points are always coplanar and a right angle measures 90º. False

Q: In the figure below, points A, B, C, and F lie on plane P. State the postulate that can be used to show each statement is true.
[Image]

A and B are collinear.
- If two points lie in a plane¸ then the entire line containing those points lies in that plane. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
- Through any two points there is exactly one line. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
- If two lines intersect¸ then their intersection is exactly one point. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
- A line contains at least two points. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
A: Through any two points there is exactly one line.

Q: In the figure below, points A, B, C, and F lie on plane P. State the postulate that can be used to show each statement is true.
[Image]

Line AD contains points A and D.
- If two lines intersect¸ then their intersection is exactly one point. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
- If two points lie in a plane¸ then the entire line containing those points lies in that plane. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
- A line contains at least two points. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
- Through any two points¸ there is exactly one line. (Postulates: 1. Through any two points, there is exactly one line. 2. Through any three points not on the same line, there is exactly one plane. 3. A line contains at least two points. 4. A plane contains at least three points not on the same line. 5. If two points lie in a plane, then the entire line containing those points lies in that plane. 6. If two lines intersect, then their intersection is exactly one point. 7. If two planes intersect, then their intersection is a line.)
A: A line contains at least two points.