chapter 2 practice test #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/... · chapter 2...

Chapter 2 Practice Test #1

Class Name : M29 Geometry - 2019-20 Term1 Instructor Name : Mr. Beckey

Student Name : _____________________ Instructor Note :

1. The first three terms of an arithmetic sequence are as follows.

, ,

Find the next two terms of this sequence.

2. The sequence of figures shows a pattern.If the pattern repeats, how many small squares will Figure 4 have?

Figure 1 Figure 2 Figure 3

3. Show that each statement is false by providing a counterexample.

(a) If the area of a rectangle is , then the length is and the width is .

Counterexample: length ______ , width ______

(b) If and are complementary angles, then one of them must have a measure less than .

Counterexample: ______ , ______

(c) If the length of is and point lies on , then and .

Counterexample: ______ , ______

(d) If the measures of , , and sum to , then one of the angles must be obtuse.

Counterexample: ______ , ______ , ______

4. There are several statements in the table below.

44 35 26

100 25 4

= =

∠ 1 ∠ 2 45 °

=m ∠ 1 ° =m ∠ 2 °

AC 26 B AC =AB 13 =BC 13

=AB =BC

∠ R ∠ S ∠ T 180 °

=m ∠ R ° =m ∠ S ° =m ∠ T °

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 2 Pr ac t i ce T es t #1 / 32

4. There are several statements in the table below. For each, determine whether it is a negation of this statement.

I am not in history class.

5. Complete the following table.

a. Consider the following statement.Josh is wearing tennis shoes.Check all the statements below that are negations of this statement.

Josh is not wearing tennis shoesIt is not the case that Josh is wearing high heelsJosh is wearing high heels

b. Consider the following conditional statement:If x is equal to the sum of two prime numbers, then x is equal to 300.What is the hypothesis of this statement?

x is equal to 300x is equal to the sum of two prime numbersx is a prime numberx is not equal to 500It is not true that x is a multiple of 10

6. Consider this conditional statement.

StatementNegation?

Yes No

I am in history class.

I am not in physics class.

I am in chemistry class.

It is not the case that I am in chemistry class.


6. Consider this conditional statement.

If an animal species is extinct, then the animal species is no longer in existence.

(a) Give the converse of the statement.

If _______ {(a) an animal species is no longer in existence, (b) an animal species is in existence, (c) ananimal species is extinct, (d) an animal species is not extinct}

then _______{(a) the animal species is no longer in existence, (b) the animal species is in existence, (c) theanimal species is extinct,(d) the animal species is not extinct}.

(b) Give the contrapositive of the statement.



(c) Give the inverse of the statement.



7. The table below gives the material of each item in Charmaine's jewelry box.These are the only items in Charmaine's jewelry box.

Item Material

Pendant Copper

Bracelet Silver

Necklace Copper

Hairpin Gold

Ring Platinum

A conditional statement is given below. Give the converse, contrapositive, and inverse of the statement. Also usethe table above to decide if each statement is true or false.

Assume that any item mentioned comes from Charmaine's jewelry box.


Given statement If an item is made from copper, then the item is a necklace.

True False

Converse

If an item is made from copper, then the item is made from copper.

If an item is made from copper, then the item is not made from copper.

If an item is made from copper, then the item is a necklace.

If an item is made from copper, then the item is not a necklace.

If an item is not made from copper, then the item is made from copper.

If an item is not made from copper, then the item is not made from copper.

If an item is not made from copper, then the item is a necklace.

If an item is not made from copper, then the item is not a necklace.

If an item is a necklace, then the item is made from copper. True False

If an item is a necklace, then the item is not made from copper.

If an item is a necklace, then the item is a necklace.

If an item is a necklace, then the item is not a necklace.

If an item is not a necklace, then the item is made from copper.

If an item is not a necklace, then the item is not made from copper.

If an item is not a necklace, then the item is a necklace.

If an item is not a necklace, then the item is not a necklace.

Contrapositive



















Inverse

If an item is made from copper, then the item is not made from copper.If an item is made from copper, then the item is a necklace.














8. The table below gives the material of each item in Latoya's jewelry box.These are the only items in Latoya's jewelry box.

Item Material

Bracelet Silver

Ring Platinum

Pendant Copper

Necklace Copper

Hairpin Gold

Complete parts (a) through (c) below.Assume that any item mentioned comes from Latoya's jewelry box.

(a) Write the following biconditional statement as a conditional statement and its converse.

Biconditional statement: An item is a pendant if and only if the item is made from copper.

Conditional statement: If an item is a pendant an item is not a pendant an item is made from copper an item is not made from copper

then the item is a pendant the item is not a pendant the item is made from copper the item is not made from copper


Converse: If an item is a pendant an item is not a pendant an item is made from copper an item is not made from copper

then the item is a pendant the item is not a pendant the item is made from copper the item is not made from copper

(b) Use the table to determine the truth value of the conditional statement and its converse.

The conditional statement is ( true / false ).

The converse is ( true / false ).

(c) Determine the truth value of the biconditional statement.

The biconditional statement is ( true / false ).

9. Suppose that the given statements are true. Find the other true statements.

Given:If the tires are old, then Elsa knows how to dance.If Elsa knows how to dance, then my favorite movie is being shown.

Which statement must also be true?- If my favorite movie is being shown, then the tires are old.- If the tires are old, then my favorite movie is being shown.- If my favorite movie is being shown, then Elsa knows how to dance.

Given:If Geometry is Carlos's favorite subject, then the dress is on sale.Geometry is Carlos's favorite subject.

Which statement must also be true?- Geometry is not Carlos's favorite subject.- The dress is on sale.- The dress is not on sale.

Given:If our instructor hates to fly, then the wall has been painted.

Which statement must also be true?- If our instructor does not hate to fly, then the wall has not been painted.- If the wall has not been painted, then our instructor does not hate to fly.- If the wall has been painted, then our instructor hates to fly.

10. Let , , and be the following statements. © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 2 Pr ac t i ce T es t #1 / 32

10. Let , , and be the following statements.

: The bake sale is on Thursday.

: Kevin is making cupcakes.

: Kevin is using the mixer.

For each argument, choose the correct symbolic form. Then determine whether the argument isvalid.

Argument Symbolic form Is the argument valid?

(a) If the bake sale is onThursday, then Kevin ismaking cupcakes. The bakesale is on Thursday.Therefore, Kevin is makingcupcakes.

Yes No

(b) If the bake sale is onThursday, then Kevin ismaking cupcakes. The bakesale is not on Thursday.Therefore, Kevin is notmaking cupcakes.

Yes No

p q r

p

q

r


11. The Venn diagram shows the memberships for the Tennis Club and the Basketball Club.Use the diagram to answer the questions below.

(a) How many people play Tennis?

(b) How many people play Tennis but not Basketball?

(c) How many people play both Tennis and Basketball?

−12

Tennis Basketball

Miguel

Aldo

Kala

Deon

Eric

Sam

Yolanda

Ali

Manuel


12. The equation is solved in several steps below.

For each step, choose the reason that best justifies it.

Step Reason

Given equation

- Addition Property of Equality- Subtraction Property of Equality- Multiplication Property of Equality- Division Property of Equality- Simplifying- Distributive Property




13. Complete the proof below by writing the correct "Reason" and, if applicable, giving the statements upon which

=−y 125 −7

−y 125

= −7

·5−y 125 = ·−7 5

−y 12 = −35

+−y 12 12 = +−35 12

y = −23


13. Complete the proof below by writing the correct "Reason" and, if applicable, giving the statements upon whichthe reason was based.

Given:

Prove:

Statement Reason

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

7. 7.

14.

Given:

Prove:

15.

=QS T V

=RS TU

=QR UV

=QS +QR RS

=T V +TU UV

=QS T V

=+QR RS +TU UV

=RS TU

=+QR TU +TU UV

=QR UV

=QT SU

=RT TU

=QR ST

Q

R

S

T

U

V

QR

S

T

U


15.

Given:

Prove:

16.

Give a pair of corresponding angles, a pair of alternate exterior angles, and a pair of alternate interior angles.

17. Two parallel lines are cut by a transversal as shown below.

=m ∠ 1 m ∠ 4=m ∠ 2 m ∠ 3

=m ∠ RST m ∠ VUT

R V

12

43

ST

U

ba

m

21

34 6

578


17. Two parallel lines are cut by a transversal as shown below.

Suppose . Find and .

18. In the figure below, . Find the values of and .

19. In the figure below, and . Find the values of and .

20.

=m ∠ 4 129 ° m ∠ 5 m ∠ 7

j l y z

m n p q x y

=2

1 234

5 678

j

h

l

61°y °+3z 1 °

p q

81°

x °−6y 63 °

m

n


20. Graph the line .

21. Find the slope of the line graphed below.

22. Find the slope of the line passing through the points and .

23. Fill in the blanks below.

=x 2

, 2 5 , 8 −4

xx

-2-4-6-8 2 4 6 8

yy

-2

-4

-6

-8

2

4

6

8

xx

-1-2-3-4-5 1 2 3 4 5

yy

-1

-2

-3

-4

-5

1

2

3

4

5


23. Fill in the blanks below.

Find the slope of the line passing through the points and .

slope:


slope:

24. Graph the line with slope passing through the point .

25. Suppose we are given the following.

, −7 6 , 2 6

, −7 9 , −7 −4

23 , −1 2

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10


25. Suppose we are given the following.

Line 1 passes through and .



(a) Find the slope of each line.

Slope of Line 1 _____



(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Line 1 and Line 2: Parallel Perpendicular Neither



26. A line passes through the point and has a slope of .

Write an equation in point-slope form for this line.

27. Consider the line .

(a) Find the equation of the line that is parallel to this line and passes through the point .

(b) Find the equation of the line that is perpendicular to this line and passes through the point .

28. The equations of three lines are given below.

, −1 4 , −3 −2, −1 −2 , 0 1, −6 −3 , 3 −6

===

, −8 9 −34

=y −47 x 1

, 7 − 3

, 7 − 3


28. The equations of three lines are given below.

Line 1:

Line 2:

Line 3:

For each pair of lines, determine whether they are parallel, perpendicular, or neither.


What is the slope of a line parallel to this line?

What is the slope of a line perpendicular to this line?


What is the slope of a line parallel to this line?

What is the slope of a line perpendicular to this line?

31. Find the slope and the -intercept of the line.

32. Find the slope and the -intercept of the line.

Write your answers in simplest form.

33. Write an equation in slope-intercept form for the line with slope and

=+6x 4y 4

=y −23 x 5

=3y +2x 5




=y +−15 x 6

=+9x 6y −6

y

=y −6x 2

y

=+6x 2y −2

2 −6© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 2 Pr ac t i ce T es t #1 / 32

33. Write an equation in slope-intercept form for the line with slope and -intercept .

34. A line passes through the point and has a slope of .

Write an equation in slope-intercept form for this line.

35. Find the line's slope and a point on the line.

slope: _____

point on the line: _____ _____

36. Write an equation of the line below.

37. Use a compass and ruler to construct the line parallel to the line through the point

2 y −6

, −8 454

=+y 1 −14 −x 5

,

xx

-1-2-3-4-5-6-7-8 1 2 3 4 5 6 7 8

yy

-1

-2

-3

-4

-5

-6

-7

-8

1

2

3

4

5

6

7

8


37. Use a compass and ruler to construct the line parallel to the line through the point .

38.

Given::

Prove:

39.

l P

=~∠ 6 ∠ 2

a b

l

P

13

24

57

68

ab


39.

Given::

Prove:

RQ SU

=~∠ 1 ∠ 4

RS V T

1

2

3 5

64

Q

R S

T

U

V


Chapter 2 Practice Test #1 Answers for class M29 Geometry -2019-20 Term1

1. , , , ,

2.

3.

(a) If the area of a rectangle is , then the length is and the width is .

Counterexample: length , width

(b) If and are complementary angles, then one of them must have a measure less than .

Counterexample: ,

(c) If the length of is and point lies on , then and .

Counterexample: ,

(d) If the measures of , , and sum to , then one of the angles must be obtuse.

Counterexample: , ,

4. There are several statements in the table below. For each, determine whether it is a negation of this statement.

I am not in history class.

5.

44 35 26 17 8

4

100 25 4

=50 =2

∠ 1 ∠ 2 45 °

=m ∠ 1 45 ° =m ∠ 2 45 °

AC 26 B AC =AB 13 =BC 13

=AB 18 =BC 8

∠ R ∠ S ∠ T 180 °

=m ∠ R 30 ° =m ∠ S 70 ° =m ∠ T 80 °

StatementNegation?

Yes No

I am in history class.

I am not in physics class.

I am in chemistry class.

It is not the case that I am in chemistry class.


5.

6.

(a) Give the converse of the statement.

If an animal species is no longer in existence,then the animal species is extinct.

(b) Give the contrapositive of the statement.

If an animal species is in existence,then the animal species is not extinct.

(c) Give the inverse of the statement.

If an animal species is not extinct,then the animal species is in existence.

7.

Given statement If an item is made from copper, then the item is a necklace.True False




(a) Consider the following statement.

Josh is wearing tennis shoes.Check all the statements below that are negations of this statement.

Josh is not wearing tennis shoes

It is not the case that Josh is wearing high heels

Josh is wearing high heels

(b) Consider the following conditional statement:

If x is equal to the sum of two prime numbers, then x is equal to 300.

What is the hypothesis of this statement?

x is equal to 300

x is equal to the sum of two prime numbers

x is a prime number

x is not equal to 500

It is not true that x is a multiple of 10


Converse














Contrapositive
























Inverse

If an item is not made from copper, then the item is a necklace.If an item is not made from copper, then the item is not a necklace.









8. (a) Write the following biconditional statement as a conditional statement and its converse.

Biconditional statement: An item is a pendant if and only if the item is made from copper.

Conditional statement: If an item is a pendant

then the item is made from copper

Converse: If an item is made from copper

then the item is a pendant

(b) Use the table to determine the truth value of the conditional statement and its converse.

The conditional statement is ( true ).

The converse is ( false ).

(c) Determine the truth value of the biconditional statement.

The biconditional statement is ( false ).

9. © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 2 Pr ac t i ce T es t #1 / 32

9.

10. Let , , and be the following statements.

: The bake sale is on Thursday.

: Kevin is making cupcakes.

: Kevin is using the mixer.

For each argument, choose the correct symbolic form. Then determine whether the argument is valid.

Argument Symbolic form Is the argument valid?

(a) If the bake sale is on Thursday,then Kevin is making cupcakes.The bake sale is on Thursday.Therefore, Kevin is makingcupcakes.

Yes No

(b) If the bake sale is on Thursday,

Given: If the tires are old, then Elsa knows how to dance.

If Elsa knows how to dance, then my favorite movie is being shown.

Which statement must also be true?

If the tires are old, then my favorite movie is being shown.

Given: If Geometry is Carlos's favorite subject, then the dress is on sale.

Geometry is Carlos's favorite subject.


The dress is on sale.

Given: If our instructor hates to fly, then the wall has been painted.


If the wall has not been painted, then our instructor does not hate to fly.

p q r

p

q

r


then Kevin is making cupcakes.The bake sale is not on Thursday.Therefore, Kevin is not makingcupcakes.

Yes No

11.

(a) How many people play Tennis?

(b) How many people play Tennis but not Basketball?

(c) How many people play both Tennis and Basketball?

12.

4

1

3


12.

Step Reason

Given equation





13.

−y 125

= −7

·5−y 125 = ·−7 5

−y 12 = −35

+−y 12 12 = +−35 12

y = −23


13.

14.

15.

16.

Statement Reason

1 =QS +QR RS Segment Addition Property

2 =TV +TU UV Segment Addition Property

3 =QS TV Given

4 =+QR RS +TU UV Substitution Property (Using 3 lines) 1 2 3

5 =RS TU Given

6 =+QR TU +TU UV Substitution Property (Using 2 lines) 4 5

7 =QR UV Addition and Subtraction Properties 6

Line(s) Used

Statement Reason Line(s) Used

1 =Q T S U Given

2 =Q T +Q R R T Segment Addition Property

3 =S U +S T T U Segment Addition Property

4 =+Q R R T +S T T U Substitution Property (Using 3 lines) 1 2 3

5 =R T T U Given

6 =+Q R T U +S T T U Substitution Property (Using 2 lines) 4 5

7 =Q R S T Addition and Subtraction Properties 6


1 =m∠ 1 m∠ 4 Given

2 =m∠ 2 m∠ 3 Given

3 =m∠ R S T +m∠ 1 m∠ 2 Angle Addition Property

4 =m∠ V U T +m∠ 3 m∠ 4 Angle Addition Property

5 =m∠ R S T +m∠ 4 m∠ 3 Substitution Property (Using 3 lines) 2 1 3

6 =m∠ R S T m∠ V U T Substitution Property (Using 2 lines) 4 5


16. Here is one possible answer.

(a) Corresponding angles: and

(b) Alternate exterior angles: and

(c) Alternate interior angles: and

17.

18.

19.

20.

21.

∠ 2 ∠ 6∠ 1 ∠ 7∠ 4 ∠ 6

=m ∠ 5 51 °=m ∠ 7 51 °

=y 119=z 20

=x 99=y 24

−34

3

xx

-2-4-6-8 2 4 6 8

yy

-2

-4

-6

-8

2

4

6

8


22.

23.


slope:


slope: Undefined

24.

25.

−32

, −7 6 , 2 60

, −7 9 , −7 −4

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10

(-1, 2)

(2, 4)


25.

(a) Find the slope of each line.

Slope of Line 1

Slope of Line 2

Slope of Line 3

(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.




26.

27.

Equation of parallel line:

Equation of perpendicular line:

28.

29.

Slope of a parallel line:

Slope of a perpendicular line:

30.

= 3= 3

= −13

=−y 9 −34 +x 8

=y −47 x 7

=y +−74 x

374




−15

5


30.

Slope of a parallel line:

Slope of a perpendicular line:

31. slope:

-intercept:

32. slope:

-intercept:

33.

34.

35.

slope:

point on the line:

36.

37.

−32

23

6y −2

−3y −1

=y −2x 6

=y +54 x 14

−14

, 5 −1

=y +−x 4


37.

38.

39.


1 =~∠ 6 ∠ 2 Given

2 a b If corr. s , then lines ∠ =~ 1


1 R Q S U Given

2 =~∠ 1 ∠ 2 If lines , then alt. int. s ∠ =~ 1

3 =~∠ 1 ∠ 4 Given

4 =~∠ 2 ∠ 4 Transitive Property 2 3

5 R S V T If corr. s , then lines ∠ =~ 4

l

P


chapter 2 practice test #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/... · chapter 2...

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