Geometry - Unit 1 Test Review, 2022

Let p represent: Anthony watches TV.

Let q represent: Anthony goes on a walk.

Translate the verbal argument into symbolic form.

If Anthony watches TV, then he will not go on a walk.

• $p\ \rightarrow\ q$

• $\sim p\rightarrow q$

• $\sim p\rightarrow\sim q$

• $p\rightarrow\sim q$

Let p represent: Luis watches TV.

Let q represent: Luis goes on a walk.

Translate the verbal argument into symbolic form.

Therefore, Luis does not go on a walk.

•  $\therefore q$  

•  $\therefore\sim q$  
  

•  $q$  
  

•  $\sim q$  

Tags

CCSS.HSS.CP.A.1

Identify the inverse of the following statement? 

If 2x = 6, then x = 3. 

•  $If\ x=3,\ then\ 2x=6.$  

•  $If\ 2x\ne6,\ then\ x\ne3.$  

•  $If\ 2x\ne6,\ then\ x=3.$  

•  $If\ x\ne3,\ then\ 2x\ne6.$  

Let p represent: Two angles sum up to 90 degrees.

Let q represent: The angles are complementary.

Translate the following verbal argument into symbolic form.

If two angles are not complementary, then the angles do not sum up to 90 degrees.

• $q\rightarrow p$

• $\sim q\rightarrow\sim p$

• $p\rightarrow q$

• $\sim p\rightarrow\sim q$

What is a valid conclusion that can be drawn from these statements using the Law of Syllogism?

If a triangle is isosceles, then it has two congruent sides.

If a triangle has two congruent sides, then it has two congruent angles.

• Therefore, the triangle has two congruent angles.

• Therefore, the triangle has two congruent sides.

• If a triangle has two congruent angles, then it is isosceles.

• If a triangle is isosceles, then it has two congruent angles.

Tags

CCSS.HSG.CO.C.10

What is the converse of the follow statement?

If Hayat drinks her cup of soda, then the cup will be empty.

• If the cup is empty, then Hayat drank her cup of soda.

• If the cup is not empty, then Hayat did not drink her cup of soda.

• If the cup is empty, then Hayat did not drink her cup of soda.

• If Hayat did not drink her cup of soda, then the cup will not be empty.

True or False. If false, provide a counterexample.

 $If\ x^2=49,\ then\ x=7.$  

• True

• False

• False, x could equal -7.

• False, x could equal 49.

Tags

CCSS.HSA.REI.B.4

Identify the contrapositive of the following logical conditional statement.

Michelle said: "If I am present in class, then I logged into my computer."

• If I did not log into my computer, then I am not present in class.

• If I logged into my computer, then I am present in class.

• If I am not present in class, then I did not log into my computer.

• If I am present in class, then I did not log into my computer.

Identify the conditional statement for the following statement.

If Alex goes outside, then it is not raining.

• If Alex goes outside, then it is raining.

• If Alex goes outside, then it is not raining.

• If Alex does not go outside, then it is raining.

• If Alex does not go outside, then it is not raining.

Tags

CCSS.HSS.CP.A.5

Convert the following statement into a biconditional.

If a shape has seven sides, then it is a heptagon.

• If a shape has seven sides if and only if then it is a heptagon.

• If a shape has seven sides if and only if it is a heptagon.

• A shape has seven sides if and only if it is a heptagon.

• A shape has seven sides if and only if then it is a heptagon.