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Geometry Reasoning Review

Total questions: 60

Worksheet time: 3hrs 1mins

Name
Class
Date
1.
What is the justification (reason)?
a)
reflexive property
b)
definition of segment bisect
c)
definition of a midpoint
d)
substitution property
2.
If <1 and <2 are complementary, then m<1 + m<2 = 90
a)
Addition POE
b)
Subtraction POE
c)
Def of right angle
d)
Def of Complementary Angles
3.
IF <ABC ≅ <DEF, then m<ABC = m<DEF
a)
Reflexive POE
b)
Addition POE
c)
Def. of congruent angles
d)
Def. of right angles
4.
If X is between R & T on a line,
then RX + XT = RT
a)
Addition POE
b)
Substitution POE
c)
Angle Addition Post.
d)
Segment Addition Post.
5.
What is the reason?
a)
Definition of Complementary
b)
Definition of 180 
c)
Definition of supplementary
d)
Angle Addition
6.
Which property justifies the next step?
a)
Segment addition postulate
b)
Definition of an angle bisector
c)
Angle addition postulate
d)
Definition of right angles
7.
Identify the  missing statement or reason
a)
Reflexive Property
b)
Definition of Midpoint
c)
Given
d)
Vertical Angles Theorem
8.
Identify the  missing statement or reason
a)
Given
b)
Vertical Angles Theorem
c)
Definition of Angle Bisector
d)
Alternate Interior Angles Theorem
9.
Identify the  missing statement or reason
a)
Definition of Angle Bisector
b)
Alternate Interior Angles Theorem
c)
Reflexive Property
d)
Definition of Midpoint
10.
What would be the correct "given" statements for this diagram?
a)
T is the midpoint of segment BG and
∡B≅∡G
b)
∡B≅∡G and ∡A≅∡W
c)
T is the midpoint of segment BG and ∡A≅∡W
d)
T is the midpoint of segment AW and ∡A≅∡W
11.
What is the "statement" for step 3 of the proof?
a)
HA=HA
b)
HA=AH
c)
MA=AM
d)
MA=MA
12.
What is the "statement" for step 3 of the proof? 
a)
∡EDA≅∡DCB
b)
∡AED≅∡BEC
c)
DE=CE
d)
∡AED≅∡CED
13.
What is the "statement" for step 2 of the proof?
a)
∆BAC≅∆DAC
b)
BC=DC
c)
∡B≅∡D
d)
∡BAC≅∡DAC
14.
What is the REASON for Statement #2?
a)
Given
b)
Definition of Complementary Angles
c)
Substitution Property
d)
Reflexive Property of Congruence
15.
What is the REASON for Statement #3?
a)
Given
b)
Definition of Complementary Angles
c)
Substitution Property
d)
Reflexive Property of Congruence
16.
What is the REASON for Statement #5?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
17.
What is the REASON for Statement #5?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
18.
Name the property.
If A is in the interior of <BDC, then m<BDA + m<ADC = m<BDC. 
a)
Reflexive
b)
Transitive
c)
Segment Addition Postulate
d)
Angle Addition Postulate
19.
Name the property.
If A is in the interior of <BDC, then m<BDA + m<ADC = m<BDC. 
a)
Reflexive
b)
Transitive
c)
Segment Addition Postulate
d)
Angle Addition Postulate
20.
Which is an example of transitive property?
a)
If a=b and b=m, then a = m.
b)
If a=b then b=a.
c)
Given a number a, a=a
d)
If a=5, then 3a-5 = 3(5)-5
21.

Given: ∠1 and ∠3 are vertical angles. What should you conclude by the vertical angles theorem?

a)

∠1\angle1  and ∠3\angle3  are a linear pair

b)

undefined andundefined are right angles.

c)

∠2≅∠3\angle2\cong\angle3  

d)

∠1≅∠3\angle1\cong\angle3  

22.

Given: ∠1 and ∠2 are supplementary. What can you conclude?

a)

m∠1+m∠2=180°m\angle1+m\angle2=180\degree

b)

m∠1+m∠2=90°m\angle1+m\angle2=90\degree

c)

m∠1=m∠2m\angle1=m\angle2

d)

Nothing

23.

What does it mean to bisect a segment or an angle?

a)

Split it into 3 equal parts.

b)

Split it into 2 equal parts.

c)

Split into 4 equal parts.

d)

Double it.

24.

In the given proof, what is the statement for step 2?

a)

Angles that form a linear pair are supplementary. m∠1+m∠3=180°m∠1+m∠3=180°  

b)

m∠3+m∠5=180°m∠3+m∠5=180°  

c)

m∠1=m∠3m∠1=m∠3  

d)

∠3≅∠5\angle3\cong\angle5  

25.

In the given proof, what is the statement for step 2?

a)

AD≅DBAD≅DB  

b)

CD≅CDCD≅CD  

c)

m∠ADC+m∠BDC=180°m\angle ADC+m\angle BDC=180\degree  

d)

∠ADC≅∠BDC\angle ADC\cong\angle BDC  

26.

In the given proof, what is the reason for step 2?

a)

Alternate Exterior Angle are Congruent

b)

Reflexive Property of Congruence

c)

Angles that form a linear pair are supplementary.

d)

Alternate Interior Angles are Congruent.

27.

Since segment BD is part of both triangles, it is congruent to itself, what do we call this?

a)

Substitution

b)

Commutative

c)

Reflexive

d)

CPCTC

28.
a)
100°
b)
80°
c)
90°
d)
180°
29.
a)
100°
b)
80°
c)
90°
d)
180°
30.
Which are pairs of vertical angles?
a)
∠COB & ∠COA
b)
∠AOD & ∠AOC
c)
∠COB & ∠AOD
d)
∠BOD & ∠AOD
31.
If LN = 32, what is MN?
a)
11
b)
20
c)
12
d)
10
32.
What is the value of x?
a)
90
b)
45
c)
180
d)
51
33.
a)
2x-6=7x+4
b)
2x-6+7x+4=90
c)
2x-6+7x+4=180
d)
2x-6+7x+4=360
34.

Given: B is the midpoint of AC. What should you conclude?

a)

AB + BC = AC

b)

AB = BC

c)

A is the segment bisector of BC

d)

ABC is a straight angle

35.

Given: <1 and <2 are a linear pair. Conclusion: m<1 + m<2 = 180. What is the reason that allows you to draw that conclusion?

a)

Angle addition postulate

b)

Definition of straight angle

c)

Linear Pair Postulate

d)

Definition of supplementary

36.

Given: AB is the segment bisector of PQ. What conclusion can you draw?

a)

PF = QF

b)

F is the midpoint of PQ

c)

m<PFA = m<QFA

d)

<PFQ is a straight angle

37.

If an angle is a straight angle, then its measure is 180°180\degree

 Given:  <ABC is a straight angle.
What conclusion can you draw?

a)

<ABC is not an acute angle

b)

<ABC is supplementary to another angle

c)

m<ABC = 180°180\degree  

d)

<ABC is a straight angle

38.

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

a)

Hypothesis: a man is 7 feet tall

Conclusion: he plays basketball

b)

Hypothesis: IF a man is 7 feet tall

Conclusion: THEN he plays basketball

c)

Hypothesis: THEN he plays basketball

Conclusion: IF a man is 7 feet tall

d)

Hypothesis: he plays basketball

Conclusion: a man is 7 feet tall

39.

Which of the following is true about the conditional statement below?

If you are in Alaska, then you are

cold.

a)

Hypothesis: you are in Alaska

Conclusion: you are

cold

b)

Hypothesis: IF you are in Alaska

Conclusion: THEN you are

cold

c)

Hypothesis: THEN you are

cold

Conclusion: IF you are in Alaska

d)

Hypothesis: you are

cold

Conclusion: you are in Alaska

40.

Which of the following is the CONVERSE of the statement below?

If an object is a ring, then it is

made of gold.

a)

If an object is made of gold, then it is a ring.

b)

If an object is not a ring, then it is not made of god.

c)

If an object is not made of gold, then it is not a ring.

d)

There is no converse of the statement.

41.

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

a)

If an object can fly, then it is a bird.

b)

If an object is not a bird, then it cannot fly

c)

If an object cannot fly, then it is not a bird

d)

There is no converse of the statement

42.

Which of the following is the INVERSE of the statement below?

If an object is a computer, then it

has a hard drive.

a)

If an object is not a computer, then it does not have a hard drive.

b)

If an object does not have a hard drive, then it is not a computer.

c)

If an object has a hard drive, then it is a computer.

d)

There is no inverse of the statement.

43.

Which of the following is the CONVERSE of the statement below?

If you play football, then you wear

a uniform.

a)

If you wear a uniform, then you play football.

b)

If you do not play football, then you do not wear a uniform.

c)

If you do not wear a uniform, then you do not play football.

d)

There is no converse of the statement.

44.

Which of the following is the INVERSE of the statement below?

If an object is a battery, then it is

rechargeable.

a)

If an object is not a battery, then it is not

rechargeable.

b)

If an object is rechargeable, then it is not a battery.

c)

If an object is not rechargeable, then it is not a battery.

d)

There is no inverse of the statement.

45.

Which of the following is the INVERSE of the statement below?

If an animal is black and white,

then it is a penguin.

a)

If an animal is not black and white, then it is not a penguin

b)

If an animal is a penguin, then it is black and white.

c)

If an animal is not a penguin, then it is not black and white.

d)

There is no inverse of the statement.

46.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a species walks on two feet, then

it is human.

a)

If a species is not human, then it does not walk on two feet.

b)

If a species is human, then it walks on two feet.

c)

If a species does not walk on two feet, then it is not human.

d)

There is no contrapositive of the statement.

47.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a gem is a ruby, then it is red.

a)

If a gem is not red, then it is not a ruby.

b)

If a gem is not a ruby, then it is not red.

c)

If a gem is red, then it is a ruby.

d)

There is no contrapositive statement.

48.

Which of the following is the BICONDITIONAL of the statement below?

If there is lightning, then there is thunder.

a)

If there is not lightning, then there is not thunder.

b)

If there is thunder, then there is lightning.

c)

There is lightning if and only if (iff) there is thunder.

d)

There is no biconditional statement.

49.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a species is a fish, then it lives in

water.

a)

If a species does not live in water, then it is not a fish.

b)

If a species is not a fish, then it does not live in water.

c)

If a species lives in water, then it is a fish.

d)

There is not contrapositive of the statement.

50.

Which of the following is a valid conditional statement for the following phrase:

An acute angle has a measure less than 90°.

a)

If an angle is acute, then it has a measure less than 90°.

b)

If an angle is not acute, then it does not have a measure less than 90°.

c)

If an angle is acute, then it is acute.

d)

If an angle does not measure less than 90°, then it is not acute.

51.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

An angle is acute if and only if (iff) it has a measure less than 90°.

a)

Biconditional

b)

Converse

c)

Inverse

d)

Contrapositive

52.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle does not have a measure less than 90°, then it is not acute.

a)

Contrapositive

b)

Converse

c)

Biconditional

d)

Inverse

53.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle has a measure less than 90°, then it is acute.

a)

Converse

b)

Contrapositive

c)

Biconditional

d)

Inverse

54.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle is not acute, then it does not have a measure less than 90°.

a)

Inverse

b)

Contrapositive

c)

Biconditional

d)

Converse

55.
When taking the converse we ___________ the hypothesis and conculsion
a)
negate
b)
switch
c)
highlight
d)
switch and negate
56.
When taking the inverse we _____________ the hypothesis and conculsion
a)
negate
b)
switch
c)
switch and negate
d)
keep the same
57.
If it is a triangle then it has three sides.
What is the hypothesis?
a)
it is a polygon
b)
it is a triangle
c)
it has three sides
d)
a triangle is a polygon
58.
Original: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
59.
What is the inverse?
If Jason does not go out to dinner, then he will come to the volleyball game.
a)
If Jason goes out to dinner, then he will not come to the volleyball game.
b)
If Jason comes to the volleyball game, then he will not go out to dinner.
c)
If Jason comes to the volleyball game, then he will go out to dinner.
d)
If Jason does not go out to dinner, then he will not come to the volleyball game.
60.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.
a)
If the measures of the angles are equal, then the angles are congruent.
b)
"If angles are not congruent, then the measures of the angles are not equal."
c)
If the measures of the angles are not equal, then the angles are not congruent.
d)
If the angles are not congruent, then the measure of the angles are equal.

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