Geometry quiz 4 – Flashcards
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Select the postulate about two planes.
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Postulate 5: If two planes intersect, then their intersection is a line.
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Select the postulate that states a line is determined by two points.
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Postulate 2: Through any two different points, exactly one line exists.
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Select the postulate that specifies the minimum number of points in space.
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Postulate 1b: Space contains at least four points not all on one plane.
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Select the postulate that states points A and B lie in only one line.
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Postulate 2: Through any two different points, exactly one line exists.
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A table with four legs will sometimes wobble if one leg is shorter than the other three, but a table with three legs will not wobble. Select the postulate that substantiates this fact.
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Postulate 3: Through any three points that are not one line, exactly one plane exists.
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State the postulate that verifies AB is in plane Q when points A and B are in Q.
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Postulate 4: If two points lie in a plane, the line containing them lies in that plane.
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Select the postulate that proves this fact. If G and H are different points in plane R, then a third point exists in R not on GH.
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Postulate 1a: A plane contains at least three points not all on one line.
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How many lines are determined by two points?
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1
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Which of the following cannot be used to state a postulate?
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theorems
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Which of the following requires a proof?
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theorem
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Two planes intersect in exactly _____.
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one line
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If a ray lays in a plane, how many points of the ray are also in the plane?
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all of the points
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A plane contains how many lines?
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infinite number of lines
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If C is between A and B then AC + CB = AB.
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always
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Three points are collinear.
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sometimes
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Two planes intersect in exactly one point.
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never
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What are axioms in algebra called in geometry?
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postulates
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Select the postulate that is illustrated for the real numbers. 5 · 1 = 5
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Multiplication identity
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Select the postulate that is illustrated for the real numbers. 3 + 2 = 2 + 3
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Commutative postulate for addition
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Select the postulate that is illustrated for the real numbers. 2(x + 3) = 2x + 6
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The distributive postulate
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Select the postulate that is illustrated for the real numbers. 25 + 0 = 25
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Additive identity
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Select the postulate that is illustrated for the real numbers. 5 + (-5) = 0
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The addition inverse postulate
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Select the postulate that is illustrated for the real numbers. 6 + 0 = 6
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The additive identity postulate
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Select the postulate that is illustrated for the real numbers. 6 · 12 = 12 · 6
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The commutative postulate for multiplication
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Select the postulate that is illustrated for the real numbers. 3x + 3 = 3(x + 1)
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The distributive postulate
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Select the postulate of equality or inequality that is illustrated. If 5 = x + 2, then x + 2 = 5
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the symmetric postulate of equality
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Select the postulate of equality or inequality that is illustrated. 3 + 2 5 and 3 + 2 = 5 are not both true.
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comparison postulate
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Select the postulate of equality or inequality that is illustrated. If a < b and b < 2, then a < 2
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the transitive postulate of inequality
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Select the postulate of equality or inequality that is illustrated. 5 = 5
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the reflexive postulate of equality
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Which of the following is proved by utilizing deductive reasoning?
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theorems
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Intersecting lines are ____________ coplanar.
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always
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Two intersecting lines have ________ of point(s) in common.
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one
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What is the minimum number of intersecting lines that lay in a plane?
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two
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How many points are used to define a plane?
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three
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Two planes intersect in a _____.
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line
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A statement that is proved by deductive logic is called a ______.
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theorem
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Which of the following best describes an indirect proof?
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Assume a statement true and then show it must be false.
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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?
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Transitive property
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Select the property of equality used to arrive at the conclusion. If 5x = 20, then x = 4.
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the division property of equality
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Select the property of equality used to arrive at the conclusion. If x = 4, then 5x = 20
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the multiplication property of equality
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Select the property of equality used to arrive at the conclusion. If x + 8 = 10, then x = 2.
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the subtraction property of equality
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Select the property of equality used to arrive at the conclusion. If x = 2, then x + 8 = 10
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the addition property of equality
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Select the property of equality used to arrive at the conclusion. If x - 3 = 7, then x = 10
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the addition property of equality
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Select the property of equality used to arrive at the conclusion. If x = 3, then x2 = 3x
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the multiplication property of equality
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Complete the conditional statement. If a + 2 < b + 3, then _____.
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a < b + 1
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Complete the conditional statement. If -2a > 6, then _____.
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a < -3
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Complete the conditional statement. If 2 > -a, then _____.
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a > -2
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If m and n are real numbers such that 4m + n = 10, then which of the following expressions represents m?
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10 minus n, divided by 4
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Sarah solves the equation as shown. 2(x + 3) = 8 1. 2x + 6 = 8 2. 2x = 2 3. x = 1 In which step did Sarah use the distributive property?
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1
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(x+2)(x+6)=0 In the problem shown, to conclude that x + 2 = 0 or x + 6 = 0, one must use the:
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zero product property
