# Geometry quiz 4 Essay

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Get AccessSelect the postulate about two planes.

Postulate 5: If two planes intersect, then their intersection is a line.

Select the postulate that states a line is determined by two points.

Postulate 2: Through any two different points, exactly one line exists.

Select the postulate that specifies the minimum number of points in space.

Postulate 1b: Space contains at least four points not all on one plane.

Select the postulate that states points A and B lie in only one line.

Postulate 2: Through any two different points, exactly one line exists.

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.

Postulate 3: Through any three points that are not one line, exactly one plane exists.

State the postulate that verifies AB is in plane Q when points A and B are in Q.

Postulate 4: If two points lie in a plane, the line containing them lies in that plane.

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.

Postulate 1a: A plane contains at least three points not all on one line.

How many lines are determined by two points?

1

Which of the following cannot be used to state a postulate?

theorems

Which of the following requires a proof?

theorem

Two planes intersect in exactly _____.

one line

If a ray lays in a plane, how many points of the ray are also in the plane?

all of the points

A plane contains how many lines?

infinite number of lines

If C is between A and B then AC + CB = AB.

always

Three points are collinear.

sometimes

Two planes intersect in exactly one point.

never

What are axioms in algebra called in geometry?

postulates

Select the postulate that is illustrated for the real numbers.

5 · 1 = 5

Multiplication identity

Select the postulate that is illustrated for the real numbers.

3 + 2 = 2 + 3

Commutative postulate for addition

Select the postulate that is illustrated for the real numbers.

2(x + 3) = 2x + 6

The distributive postulate

Select the postulate that is illustrated for the real numbers.

25 + 0 = 25

Additive identity

Select the postulate that is illustrated for the real numbers.

5 + (-5) = 0

The addition inverse postulate

Select the postulate that is illustrated for the real numbers.

6 + 0 = 6

The additive identity postulate

Select the postulate that is illustrated for the real numbers.

6 · 12 = 12 · 6

The commutative postulate for multiplication

Select the postulate that is illustrated for the real numbers.

3x + 3 = 3(x + 1)

The distributive postulate

Select the postulate of equality or inequality that is illustrated.

If 5 = x + 2, then x + 2 = 5

the symmetric postulate of equality

Select the postulate of equality or inequality that is illustrated.

3 + 2 5 and 3 + 2 = 5 are not both true.

comparison postulate

Select the postulate of equality or inequality that is illustrated.

If a < b and b < 2, then a < 2

the transitive postulate of inequality

Select the postulate of equality or inequality that is illustrated.

5 = 5

the reflexive postulate of equality

Which of the following is proved by utilizing deductive reasoning?

theorems

Intersecting lines are ____________ coplanar.

always

Two intersecting lines have ________ of point(s) in common.

one

What is the minimum number of intersecting lines that lay in a plane?

two

How many points are used to define a plane?

three

Two planes intersect in a _____.

line

A statement that is proved by deductive logic is called a ______.

theorem

Which of the following best describes an indirect proof?

Assume a statement true and then show it must be false.

Al is taller than Bob, and Bob is taller than Carl. Which property would you use to prove that Al is taller than Carl?

Transitive property

Select the property of equality used to arrive at the conclusion.

If 5x = 20, then x = 4.

the division property of equality

Select the property of equality used to arrive at the conclusion.

If x = 4, then 5x = 20

the multiplication property of equality

Select the property of equality used to arrive at the conclusion.

If x + 8 = 10, then x = 2.

the subtraction property of equality

Select the property of equality used to arrive at the conclusion.

If x = 2, then x + 8 = 10

the addition property of equality

Select the property of equality used to arrive at the conclusion.

If x – 3 = 7, then x = 10

the addition property of equality

Select the property of equality used to arrive at the conclusion.

If x = 3, then x2 = 3x

the multiplication property of equality

Complete the conditional statement.

If a + 2 < b + 3, then _____.

If a + 2 < b + 3, then _____.

a < b + 1

Complete the conditional statement.

If -2a > 6, then _____.

If -2a > 6, then _____.

a < -3

Complete the conditional statement.

If 2 > -a, then _____.

If 2 > -a, then _____.

a > -2

If m and n are real numbers such that 4m + n = 10, then which of the following expressions represents m?

10 minus n, divided by 4

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?

2(x + 3) = 8

1. 2x + 6 = 8

2. 2x = 2

3. x = 1

In which step did Sarah use the distributive property?

1

(x+2)(x+6)=0

In the problem shown, to conclude that x + 2 = 0 or x + 6 = 0, one must use the:

zero product property