Unit 2 Review

Unit 2 Review

Section 2.1

Fill in the Blanks

Fill in the Blanks

Multiple Choice

What is the hypothesis in the following conditional statement:

If a polygon is a hexagon, then it has six sides.

• a polygon is a hexagon

• if a polygon is a hexagon

• it has six sides

• then it has six sides

Multiple Choice

What is the conclusion in the following statement:

If it is raining outside, then I will wear my raincoat.

• I will wear my raincoat

• then I will wear my raincoat

• it is raining outside

• if it is raining outside

Multiple Select

Select all that are true:

• The conditional and the contrapositive have the same truth values

• The converse and the inverse have the same truth values

• The conditional and the converse have the same truth values

• The conditional and the inverse have the same truth values

Multiple Choice

What is the inverse?

• p --> q

• q --> p

• ~p --> ~q

• ~q --> ~p

Section 2.2

Multiple Choice

Describe the pattern

• Each regular polygon has one more side than the previous figure.

• The figures have a total area that is decreasing by 1 square unit.

• These are irregular polygons that increase in perimeter with each polygon.

• Both the side length and the total area are one unit more than the previous figure.

Multiple Choice

The previous question asked what the pattern was, and the correct answer was "Each regular polygon has one more side than the previous figure." What type of logic is being used here?

• Inductive Reasoning

• Deductive Reasoning

• The Law of Syllogism

• The Law of Detachment

Multiple Choice

Use the Law of Detachment to determine what you can conclude:

If a triangle has equal side lengths, then each interior angle measure is 

 $60\degree$  . Triangle ABC has equal side lengths.

• Therefore, each interior angle measure is 60 degrees.

• Then the conditional must be true.

• We can conclude nothing from this, as the Law of Detachment does not apply.

• Then the conditional must be false.

Multiple Choice

Use the Law of Syllogism to write a new conditional statement that follows from the true statements:

If x > 1, then 3x > 3.
If 3x > 3, then

 $(3x)^2\ >\ 9$  

• If x > 1, then  $(3x)^2\ >\ 9$  

• If  $(3x)^2\ >\ 9$  , then 3x > 3

•  $(3x)^2\ >\ 9$  , then x > 1

• The Law of syllogism does not apply here.

Multiple Choice

Select the counterexample that shows that the conjecture is false:

Conjecture: A line s divides line segment MN into two line segments. So, the line s is the segment bisector of MN.

• If another line also divides MN, then line s is not the only segment bisector of MN.

• Line s must intersect MN at a right angle in order to be the segment bisector of MN.

• If line s intersects MN anywhere besides the midpoint, it is not the segment bisector of MN.

• If line s intersects MN at the midpoint, it is the perpendicular bisector of MN.

Section 2.3

Multiple Choice

Which postulate is being shown?

• Two-Point Postulate

• Line-Point Postulate

• Line Intersection Postulate

• Three-Point Postulate

Open Ended

Use the diagram to write an example of the three-point postulate.

Multiple Choice

Which postulate is being demonstrated here?

• Three-Point Postulate

• Plane-Point Postulate

• Plane-Line Postulate

• Plane Intersection Postulate

Multiple Choice

Assume that Points A and B are placed on an already existing line. Which postulate is being shown here?

• Two-Point Postulate

• Line-Point Postulate

• Line Intersection postulate

• Plane-Point Postulate

Section 2.4

Open Ended

Write the first step of the proof for this problem, alongside the reason:

Given:  $3x+2\ =20$  

Prove:  $x\ =\ 6$  

Open Ended

Write the second step of the proof for this problem, alongside the reason:

Given:  $3x+2\ =20$  

Prove:  $x\ =\ 6$  

1.  $3x+2\ =20$  , given

Open Ended

Write the third step of the proof for this problem, alongside the reason:

Given:  $3x\ =18$  

Prove:  $x\ =\ 6$  

1.  $3x\ =18$ , given
2.  $3x\ =18$ , Subtraction Property of Equality

Multiple Choice

Which of these describes the Symmetric Property of Equality?

• If a=b, then b=a

• a=a

• If a=b and b=c, then a=c

• If a=b, then a can be substituted for b in any equation or expression.