Deductive Reasoning in Geometry

What does deductive reasoning use to form a logical argument?

• Personal experiences

• Opinions and beliefs

• Facts, definitions, properties, and laws of logic

• Random guesses

According to the law of detachment, if the hypothesis of a true conditional statement is true, what can be said about the conclusion?

• The conclusion is false

• The conclusion is uncertain

• The conclusion must also be true

• The conclusion is irrelevant

If two segments have the same length, what can be concluded about them?

• They are equal

• They are parallel

• They are congruent

• They are perpendicular

If Mary goes to the movies every Friday and today is Friday, what can be concluded?

• Mary will visit a friend

• Mary will go to the movies

• Mary will go shopping

• Mary will stay home

What is the law of syllogism?

• Combining multiple hypotheses into one

• Combining multiple conclusions into one

• Combining multiple conditional statements into one

• Combining multiple definitions into one

If Rick takes chemistry this year and Jessie is Rick's lab partner, what can be concluded?

• Rick will drop chemistry

• Rick will get an A in chemistry

• Rick will switch lab partners

• Rick will fail chemistry

Using the law of detachment, if angle R is 155 degrees, what can be concluded about angle R?

• Angle R is straight

• Angle R is acute

• Angle R is right

• Angle R is obtuse

If Janelle gets a job, what can she afford?

• A house

• A vacation

• A car

• A pet

If Janelle can afford a car, what will she do?

• Sell the car

• Drive to school

• Walk to school

• Take the bus

Combining the statements: 'If Janelle gets a job, she can afford a car' and 'If Janelle can afford a car, she will drive to school', what is the new statement?

• If Janelle gets a job, she will drive to school

• If Janelle gets a job, she will take the bus

• If Janelle gets a job, she will walk to school

• If Janelle gets a job, she will sell the car