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What is the postulate about two planes?
What is the postulate about two planes?
Which postulate states that a line is determined by two points?
Which postulate states that a line is determined by two points?
Which postulate specifies the minimum number of points in space?
Which postulate specifies the minimum number of points in space?
Which postulate states that points A and B lie in only one line?
Which postulate states that points A and B lie in only one line?
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What does a table with four legs sometimes wobble if one leg is shorter than the other three substantiate?
What does a table with four legs sometimes wobble if one leg is shorter than the other three substantiate?
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State the postulate that verifies AB is in plane Q when points A and B are in Q.
State the postulate that verifies AB is in plane Q when points A and B are in Q.
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Select the postulate that proves that if G and H are different points in plane R, then a third point exists in R not on GH.
Select the postulate that proves that if G and H are different points in plane R, then a third point exists in R not on GH.
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How many lines are determined by two points?
How many lines are determined by two points?
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Which of the following cannot be used to state a postulate?
Which of the following cannot be used to state a postulate?
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Which of the following requires a proof?
Which of the following requires a proof?
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Two planes intersect in exactly _____?
Two planes intersect in exactly _____?
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If a ray lies in a plane, how many points of the ray are also in the plane?
If a ray lies in a plane, how many points of the ray are also in the plane?
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A plane contains how many lines?
A plane contains how many lines?
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If C is between A and B then AC + CB = AB.
If C is between A and B then AC + CB = AB.
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Three points are collinear.
Three points are collinear.
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Two planes intersect in exactly one point.
Two planes intersect in exactly one point.
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What are axioms in algebra called in geometry?
What are axioms in algebra called in geometry?
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Select the postulate that is illustrated for the real numbers: 5 · 1 = 5.
Select the postulate that is illustrated for the real numbers: 5 · 1 = 5.
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Select the postulate illustrated for the real numbers: 3 + 2 = 2 + 3.
Select the postulate illustrated for the real numbers: 3 + 2 = 2 + 3.
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Select the postulate illustrated for the real numbers: 2(x + 3) = 2x + 6.
Select the postulate illustrated for the real numbers: 2(x + 3) = 2x + 6.
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Select the postulate illustrated for the real numbers: 25 + 0 = 25.
Select the postulate illustrated for the real numbers: 25 + 0 = 25.
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Select the postulate illustrated for the real numbers: 5 + (-5) = 0.
Select the postulate illustrated for the real numbers: 5 + (-5) = 0.
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Select the postulate illustrated for the real numbers: 6 + 0 = 6.
Select the postulate illustrated for the real numbers: 6 + 0 = 6.
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Select the postulate illustrated for the real numbers: 6 · 12 = 12 · 6.
Select the postulate illustrated for the real numbers: 6 · 12 = 12 · 6.
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Select the postulate illustrated for the real numbers: 3x + 3 = 3(x + 1).
Select the postulate illustrated for the real numbers: 3x + 3 = 3(x + 1).
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What is the postulate of equality or inequality illustrated by if 5 = x + 2, then x + 2 = 5?
What is the postulate of equality or inequality illustrated by if 5 = x + 2, then x + 2 = 5?
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Which is the postulate illustrated by '3 + 2 = 5 and 3 + 2 > 5'?
Which is the postulate illustrated by '3 + 2 = 5 and 3 + 2 > 5'?
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What is the postulate illustrated by if a < b and b < 2, then a < 2?
What is the postulate illustrated by if a < b and b < 2, then a < 2?
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What is the postulate illustrated by if 5 = 5?
What is the postulate illustrated by if 5 = 5?
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Which of the following is proved by utilizing deductive reasoning?
Which of the following is proved by utilizing deductive reasoning?
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Intersecting lines are ____________ coplanar.
Intersecting lines are ____________ coplanar.
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Two intersecting lines have ________ of point(s) in common.
Two intersecting lines have ________ of point(s) in common.
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What is the minimum number of intersecting lines that lay in a plane?
What is the minimum number of intersecting lines that lay in a plane?
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How many points are used to define a plane?
How many points are used to define a plane?
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Two planes intersect in a _____?
Two planes intersect in a _____?
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A statement that is proved by deductive logic is called a _____?
A statement that is proved by deductive logic is called a _____?
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Which of the following best describes an indirect proof?
Which of the following best describes an indirect proof?
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Al is taller than Bob, and Bob is taller than Carl. Which property would you use to prove that Al is taller than Carl?
Al is taller than Bob, and Bob is taller than Carl. Which property would you use to prove that Al is taller than Carl?
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Select the property of equality used to arrive at the conclusion: If 5x = 20, then x = 4.
Select the property of equality used to arrive at the conclusion: If 5x = 20, then x = 4.
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Select the property of equality used to arrive at the conclusion: If x = 4, then 5x = 20.
Select the property of equality used to arrive at the conclusion: If x = 4, then 5x = 20.
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Select the property of equality used to arrive at the conclusion: If x + 8 = 10, then x = 2.
Select the property of equality used to arrive at the conclusion: If x + 8 = 10, then x = 2.
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Select the property of equality used to arrive at the conclusion: If x = 2, then x + 8 = 10.
Select the property of equality used to arrive at the conclusion: If x = 2, then x + 8 = 10.
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Select the property of equality used to arrive at the conclusion: If x - 3 = 7, then x = 10.
Select the property of equality used to arrive at the conclusion: If x - 3 = 7, then x = 10.
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Select the property of equality used to arrive at the conclusion: If x = 3, then x² = 3x.
Select the property of equality used to arrive at the conclusion: If x = 3, then x² = 3x.
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Complete the conditional statement: If a + 2 < b + 3, then _____.
Complete the conditional statement: If a + 2 < b + 3, then _____.
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Complete the conditional statement: If -2a > 6, then _____.
Complete the conditional statement: If -2a > 6, then _____.
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Complete the conditional statement: If 2 > -a, then _____.
Complete the conditional statement: If 2 > -a, then _____.
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If m and n are real numbers such that 4m + n = 10, then which expression represents m?
If m and n are real numbers such that 4m + n = 10, then which expression represents m?
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In the equation 2(x + 3) = 8, in which step did Sarah use the distributive property?
In the equation 2(x + 3) = 8, in which step did Sarah use the distributive property?
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In the problem (x+2)(x+6)=0, to conclude that x + 2 = 0 or x + 6 = 0, one must use the:
In the problem (x+2)(x+6)=0, to conclude that x + 2 = 0 or x + 6 = 0, one must use the:
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Study Notes
Postulates in Geometry
- Postulate 5: If two planes intersect, their intersection is a line.
- Postulate 2: Through any two distinct points, exactly one line exists.
- Postulate 1b: Space contains at least four points not all in one plane.
- Postulate 4: If two points lie in a plane, the line containing them also lies in that plane.
- Postulate 1a: A plane contains at least three points not all on one line.
Properties of Lines and Planes
- A table with three legs will not wobble, while one with four legs can if one leg is shorter. This relates to Postulate 3 about planes containing three points.
- Infinite lines can exist in a single plane.
- Two planes can intersect in one line, while two intersecting lines share exactly one point.
- All points on a ray that lies in a plane are also in that plane.
Theorems and Proofs
- Theorems require proof while postulates are assumed truths.
- Deductive reasoning is used to prove theorems.
- Properties of equality include:
- Symmetric Postulate: If (5 = x + 2), then (x + 2 = 5).
- Transitive Property: If (a < b) and (b < 2), then (a < 2).
- Division Property: If (5x = 20), then (x = 4).
- Addition Property: If (x = 2), then (x + 8 = 10).
Algebraic Postulates
- Multiplication Identity: (5 \cdot 1 = 5).
- Commutative Postulate for Addition: (3 + 2 = 2 + 3).
- Additive Identity: (25 + 0 = 25).
- Distributive Postulate: (2(x + 3) = 2x + 6).
- Zero Product Property is used to conclude that if ((x + 2)(x + 6) = 0), then (x + 2 = 0) or (x + 6 = 0).
Definitions and Conditional Statements
- The relationship between angles or lengths can be expressed using conditional statements, such as If (a + 2 < b + 3), then (a < b + 1).
- The concept of collinearity states that three points are collinear "sometimes."
Indirect Proofs
- An indirect proof assumes a statement is true and shows it leads to a contradiction.
Intersecting Lines and Points
- Two intersecting lines are always coplanar, as they share a common plane.
- The minimum number of intersecting lines in a plane is two, and at least three points are required to define a plane.
These study notes summarize foundational postulates and properties in geometry, and highlight the principles governing lines, planes, and their intersections.
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Description
Test your knowledge of key postulates in geometry with this quiz. Explore the foundational principles that govern lines and planes. Perfect for reinforcing your understanding of geometric concepts.
