Geometry Conditionals and Counterexamples

Geometry Exam 1 Study Guide and Review

by Robert Tinaro

​Unit 1: Geometry Basics

• ​undefined terms of geometry and postulates

• ​Definitions, notation, and names: points, lines, planes, segments, rays, midpoints, bisectors, angles, and angle bisectors

• ​segment addition and midpoint problem solving

• ​opposite rays and angles formed by intersecting lines

• ​angle relationships and special angle pairs

Multiple Choice

The three undefined terms of geometry are: 

• points, lines and planes

• lines, segments, and rays

• collinear, coplanar, shapes

• postulates, theorems, and definitions

Multiple Choice

Two lines intersect at a ....

• angle
• point
• line
• intersection

Multiple Choice

Two planes intersect at a...

• line
• point
• plane
• letter

Multiple Choice

Points that lie on the same line are _________.

• coplanar
• collinear
• parallel
• perpendicular

Multiple Choice

Name the intersection of Line c and Plane R

• Point J
• Line HK
• Point K
• Line MN

Multiple Choice

ALWAYS, SOMETIMES or NEVER:

Through any three points, there exists exactly one line.

• Always

• Sometimes

• Never

Multiple Choice

A rule that is accepted without proof

• postulate
• theorem
• proof
• conditional statement

Multiple Select

A ________ has at least three __________ points.

• plane; collinear

• line; collinear

• plane; non-collinear

• line; non-collinear

Multiple Choice

Name the figure using geometric notation.

• $$\overrightarrow{SR}$$

• $$\overline{RS}$$

• $$\overrightarrow{RS}$$

Multiple Choice

Name the figure using geometric notation.

• $$\overline{QR}$$

• $$\overrightarrow{RQ}$$

• $$\overrightarrow{QR}$$

Multiple Choice

Name the OPPOSITE RAYS using geometric notation.

• $$\overrightarrow{FE}$$ and $$\overrightarrow{FG}$$

• $$\overrightarrow{EF}$$ and $$\overrightarrow{FG}$$

• $$\overleftarrow{FE}$$ and $$\overrightarrow{FG}$$

Multiple Choice

Choose the correct name for the angle marked  $$\angle4.$$  

• $$\angle K$$  

• $$\angle KVJ$$  

• $$\angle LVK$$  

• $$\angle JKV$$  

Multiple Choice

What is the correct definition of an angle? 

• one single ray
• two rays that meet at a single endpoint (vertex)
• two lines that never intersect
• two rays that go in opposite directions

Multiple Choice

Solve for x

• x = 77
• x = 7.5
• x = 8
• x = 18

Multiple Choice

D is the midpoint of EF.
ED = 4x + 6
DF = 7x -9
 Find EF.

• 5
• 26
• 52
• 22

Multiple Choice

Find MK.

• 6

• 4

• 14

• 8

Multiple Choice

B is the midpoint of AC.  Find AB.

• 2
• 16
• 8
• 4

Multiple Choice

AND find the measure of ∠ABD

• x=3/17 ∠ABD = 27°

• x=9 ∠ABD = 81°

• x=3 ∠ABD = 27°

• x= -3 ∠ABD = -27°

Multiple Choice

Which angle is complementary to $$\angle LJM$$  

• $$\angle MJN$$  

• $$\angle NJP$$  

• $$\angle FGE$$  

• $$\angle LJK$$  

Multiple Choice

Which of the following equations will solve the problem:

An angle is 12 less than 3 times the supplement. Find the measure of the angle and its supplement.

• x + 3x-12=180

• x = 3(180 - x) - 12

• x = 3(x - 12)

• x + 3(x - 12) = 180

Multiple Choice

$$\overline{AB}\ \perp\ \overline{BC}\ and\ point\ D\ lies\ in\ the\ interior\ of\ \angle ABC.\ Ifm\angle ABD\ =\left(3x\ -\ 2\right)\degree\ and\ m\angle DBC\ =\ \left(2x\ +\ 17\right)\degree,\ then\ find\ the\ value\ of\ x\ and\ the\ m\angle\ ABC.$$  

Which of the following equations correctly finds the value of x.

• 90 - 3x - 2 = 2x + 17

• 3x - 2 = 2x + 17

• 3x - 2 = 90

• 3x - 2 + 2x 17 = 90

​Unit 2: Logic, Reasoning and Proof

• ​inductive verses deductive reasoning

• ​conditionals and converses

• ​counterexamples

• ​segment addition proofs

• ​angle addition proofs

Multiple Choice

The type of reasoning where a person makes  conclusions based on observations and patterns is called...

• Inductive reasoning
• Deductive reasoning
• Conjecture
• Experiments

Multiple Choice

What is a conjecture?

• A statement believed to be true based on observations.
• An example which disproves an hypothesis.
• the performance of tricks that are seemingly magical

Multiple Choice

Used to prove that a conjecture is false.

• Counterexample
• Inductive Reasoning
• Concluding statement
• Conjecture

Multiple Choice

Which number is a counterexample to the following statement? : 
All numbers that are divisible by 2 are divisible by 4

• 0
• 12
• 28
• 42

Multiple Choice

What does deductive reasoning use to form its arguments?

• patterns

• specific cases

• observed examples

• facts, definitions, accepted properties, and laws of logic

Multiple Choice

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

• It is not Friday
• It is Friday
• I will not get paid
• I will get paid

Multiple Choice

For the converse we _________ the hypothesis and conclusion

• switch
• negate
• switch and negate

Multiple Choice

p→q
What is the converse?

• q→p
• ∼p→∼q
• ∼q→∼p
• p→∼q

Multiple Choice

What is the converse to this statement?

• If it isn't dark outside, then it is not night.
• If it is night, then it is dark outside
• If it is not night, then it is not dark outside.
• It is night.

Multiple Choice

Fill in the reason for 5. 

• Addition Postulate
• Substitution property
• Definition of midpoint
• Segment Addition Postulate

Multiple Choice

Fill in the statement for number 4. 

• RA=RE +AE
• EL = EA + AL
• RE +EA= EA +AL
• RA = EL

Multiple Choice

Fill in the reason for number 3. 

• Reflexive property
• Symmetric Property
• Transitive property
• Substitution property

Multiple Choice

Fill in the statement for number 3. 

• HA = AY
• HA = AP
• A is the midpoint of HP

Multiple Choice

Which of the following is an example of the transitive property?

• If x = 5 and and x = y, then y = 5.

• If x = y then y = x

• x = x

• If 2x + 4 = 2, then x = -1

Multiple Choice

What is the reason?

• Transitive 
• Substitution
• Middle Man
• Replacing 

Multiple Choice

Name the property of equality or congruence that justifies going from the first statement to the second statement.

• Reflexive Property of Congruence
• Symmetric Property of Congruence
• Distributive Property
• Transitive Property of Congruence

Multiple Choice

What is the justification?

• Definition of congruence

• Reflexive Property of Congruence

• Segment Addition Postulate

• Definition of Midpoint

Multiple Choice

Choose the best option to fill in the blank:

• Addition Property of Equality

• Subtraction Property of Equality

• Substitution Property of Equality

• Complementary Angles are Congruent

Multiple Choice

Choose the best Reason to fill in the blank in the two-column proof:

• Substitution Property

• Symmetric Property

• Transitive Property

• Reflexive Property

Multiple Choice

Which best fills in the blank on Statement 3 ?

• RS + RS = RT

• ST + ST = RT

• RS + ST = RT

• RS = ST

Multiple Choice

What Reason is correct to fill in Reason 5 ?

• Congruent Complements Theorem

• Congruent Supplements Theorem

• Definition of Complementary

• Definition of Congruence