Download - Chapter 4 Practice Test #1 - M2 Mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/... · 5 ECD=~ BCA SAS Congruence Property 1 3 4 Statement Reason Line(s) Used 1 EF GD Given 2∠EFD=~∠GDF

Chapter 4 Practice Test #1

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

Student Name : _____________________ Instructor Note :

1. Find the value of .

2. Find the value of .

3. In the triangle below, with right angle , suppose that and .

Find the degree measure of each angle in the triangle.

4. Find .

5. Are the triangles below acute, obtuse, or right?

x

x

∠R =m∠Q +2x 16 ° =m∠S +3x 4 °

x

82 °

x °67 °

56 °

133 ° x °

+3 x 4 °

+2x 16 °

R S

Q

114 °

x °

39 °42°

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 4 Pr ac t i ce T es t #1 / 15

5. Are the triangles below acute, obtuse, or right?

Triangle A Triangle B

Triangle C Triangle D

6. The triangles below are congruent and their corresponding parts are marked.

Name all the corresponding congruent angles and sides.Then, complete the triangle congruence statement.

(a) (b)

(c)

7. Consider and in the figure below.

Acute Obtuse Right

Triangle A

Triangle B

Triangle C

Triangle D

=~∠A ∠ =~AB

=~∠B ∠ =~AC

=~∠C ∠ =~BC

=~CAB

HIJ LKJ

60°

60°

60°

120° 30°

30°

55°

35°

40°

30°110°

A

B

C

Y

Z

X


7. Consider and in the figure below.

Use the figure above to complete the following.

8. Use the given information to prove that .

Given:

Prove:

9.

Given:

Prove:

10. The segment was constructed so that it bisects

HIJ LKJ

(a) and have been separated. Fill in the missing vertex labels.HIJ LKJ

10

2

7

1

(b) Choose the correct statement below about and .

Then fill in the additional information as necessary.

HIJ LKJ

The triangles have a common side.

Common side: { , , , , , }HI HJ IJ JK JL KL

The triangles have a common angle.

Common angle: { , , , , , , , , , }∠1 ∠2 ∠3 ∠4 ∠5 ∠6 ∠7 ∠8 ∠9 ∠10The triangles have neither a common side nor a common angle.

=~PQR STR

=~QR TR

=~PR SR

=~PQR STR

Statement Reason

1 =~QR Given

2 =~PR SR _________________

3 =~∠ PRQ ∠ Vertical Angles Property

4 =~PQR STR _________________ 1 2 3

Line(s) Used

=~BC DC

=~AC EC

=~ABC EDC

H

I

J

L

K

8

109 5

76

3

14

2

P

Q

R

S

T

A

BC

D

E


10. The segment was constructed so that it bisects .

11. For each figure below, determine (by using the markings) if there is a pair of congruent triangles. If there is, name the congruence and give the property justifying the congruence.

Note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn in determining your answers.

(a)

Not Necessarily Congruent

Congruent :

________

by the (SAS | SSS | AAS | ASA) Congruence Property

(b)


Congruent :

________


(c)


Congruent :

________


12.

YP ∠XYZ

Based on the construction, choose the statement(s) that must be true.Choose all that apply.

=~YM XM

=~YX YP

=~YM YN

=~YQ XM

=~∠XYP ∠ZYP

None of these must be true.

=~MNO

=~UVW

=~GHI

Y

X

Z

M

N

P

Q

M

N

OQ

P

R

U

V

W Y

X

Z

G

H

I

K

J

L


12.

Given:

bisects

Prove:

13.

Given:

Prove:

14.

Given: is the midpoint of

Prove:

15. Use the given information to prove that

=~DC AC

DA EB

=~ECD BCA

EF GD

FG DE

=~DEF FGD

C EB

DE AB

=~DC AC

~DEF DGF

C

A

B

D

E

D

E

G

F

C

A

B

D

E



Given: is a right angle

is a right angle

Prove:

16.

Given:

Prove:

17.

18. Each part below contains one triangle and one figure that can be adjusted to make a triangle. The markings indicate congruence.

=~DEF DGF

∠DFE

∠DFG

=~∠DEF ∠DGF

=~DEF DGF

Statement Reason

1 is a right angle∠ DFE Given

2 is a right angle∠ DFG Given

3 =~∠ DFE ∠ DFG _________________ 1 2

4 =~∠ DEF ∠ Given

5 =~DF Reflexive Property

6 =~DEF DGF _________________ 3 4 5

Line(s) Used

=~EF GF

=~∠DEF ∠HGF

=~DEF HGF

=~BC DC

=~∠BAC ∠DEC

=~AB ED

D

E

F

G

D

E

F

G H

A

B

C

D E


18. Each part below contains one triangle and one figure that can be adjusted to make a triangle. The markings indicate congruence.

19. For each pair of triangles, determine whether the Hypotenuse-Leg (HL) Congruence Property can be used to prove that the triangles are congruent.

20. Use the given information to prove that

(a) Adjust the figure on the right to explore the different triangles that can beformed. Then answer the question. Note that the figure will not be graded.

Which of the following is true?

The two triangles must be congruent.

Reason: 'Side-Angle-Side (SAS) Congruence Property' , 'Angle-Side-Angle (ASA) Congruence Property' , 'Side-Side-Side (SSS) Congruence Property' , 'Angle-Angle-Side (AAS) Congruence Property'

The two triangles do not have to be congruent.

(b) Adjust the figure on the right to explore the different triangles that can beformed. Then answer the question. Note that the figure will not be graded.



Reason: 'Side-Angle-Side (SAS) Congruence Property' , 'Angle-Side-Angle (ASA) Congruence Property' , 'Side-Side-Side (SSS) Congruence Property' , 'Angle-Angle-Side (AAS) Congruence Property'


(a)

16 cm 16 cm

(b)

Can the HL CongruenceProperty be used?

Yes No Yes No

(c) (d)


Yes No Yes No

~WYZ WXZ© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 4 Pr ac t i ce T es t #1 / 15


Given: and are right triangles

Prove:

21. For each part below, use the figure to fill in the blank. If necessary, you may learn what the markings on a figure indicate.

(a) Find . (b) Find .

______ ______

22. Suppose that is isosceles with base .

Suppose also that and .

Find the degree measure of each angle in the triangle.

23. Use the given information to complete the proof of the following theorem.

=~WYZ WXZ

WYZ WXZ

=~XZ YZ

=~WYZ WXZ

m∠Q m∠M

=m∠Q ° =m∠M °

VWX VX

=m∠V +4x 25 ° =m∠W +2x 40 °

W

X

Y

Z

Q

R

S

8 830 °

M N

P

+4x 25 °

+2x 40 °

W

V X


23. Use the given information to complete the proof of the following theorem.

The angles opposite the two congruent sides of an isosceles triangle are congruent.

Given:

bisects

Prove:

24. Parallelogram is shown below. Give the coordinates of .

25. Determine whether a triangle with the given vertices is a right triangle.

=~QP QR

QS ∠PQR

=~∠P ∠R

RSTU T

Righttriangle

Not a righttriangle

Cannot bedetermined

, , D , 1 −2 E , −1 4 F , 5 6

, , J , −3 1 K , 1 7 L , 8 0

, , A , 4 11 B , 2 −12 C , −8 −4

Q

P

R

S

xx

yy

R(0, 0) U(h, 0)

T(?, ?)S(-f, g)


Chapter 4 Practice Test #1 Answers for class M29 Geometry - 2019-20 Term1

1.

2.

3.

4.

5.

6.

(a) (b)

(c)

7.

8.

=x 31

=x 77

=m∠Q 44°=m∠R 90°=m∠S 46°

=x 33

Acute Obtuse Right

Triangle A

Triangle B

Triangle C

Triangle D

=~∠A ∠Y =~AB YZ

=~∠B ∠Z =~AC YX

=~∠C ∠X =~BC ZX

=~CAB XYZ

(a) and have been separated. Fill in the missing vertex labels.HIJ LKJ

10

2

7

1

(b) Choose the correct statement below about and .

Then fill in the additional information as necessary.

HIJ LKJ

The triangles have a common side.

Common side: ▼(Choose one)

The triangles have a common angle.

Common angle:

The triangles have neither a common side nor a common angle.


8.

9.

10.

11.

Statement Reason

1 =~QR TR Given

2 =~PR SR _________________

3 g i v en Vertical Angles Property

4 =~PQR STR _________________ 1 2 3

Line(s) Used

Statement Reason Line(s) Used

1 =~B C D C Given

2 =~A C E C Given

3 =~∠ A C B ∠ E C D Vertical Angles Property

4 =~A B C E D C SAS Congruence Property 1 2 3

Based on the construction, choose the statement(s) that must be true.Choose all that apply.

=~YM XM

=~YX YP

=~YM YN

=~YQ XM

=~∠XYP ∠ZYP

None of these must be true.


11. (a)

Not Necessarily Congruent Congruent :

QPRby the (SSS) Congruence Property

(b)


________by the (_____) Congruence Property

(c)


KJLby the (AAS) Congruence Property

12.

13.

14.

=~MNO

=~UVW

=~GHI


1 =~D C A C Given

2 bisectsD A E B Given

3 =~E C B C Definition of Segment Bisector 2

4 =~∠ E C D ∠ B C A Vertical Angles Property

5 =~E C D B C A SAS Congruence Property 1 3 4


1 E F G D Given

2 =~∠ E F D ∠ G D F If lines , then alt. int. s ∠ =~ 1

3 F G D E Given

4 =~∠ E D F ∠ G F D If lines , then alt. int. s ∠ =~ 3

5 =~D F D F Reflexive Property

6 =~D E F F G D ASA Congruence Property 2 4 5

M

N

OQ

P

R

U

V

W Y

X

Z

G

H

I

K

J

L


14.

15.

16.

17.

18.


1 is the midpoint ofC E B Given

2 =~E C B C Definition of Midpoint 1

3 D E A B Given

4 =~∠ D E C ∠ A B C If lines , then alt. int. s ∠ =~ 3

5 =~∠ E C D ∠ B C A Vertical Angles Property

6 =~E C D B C A ASA Congruence Property 2 4 5

7 =~D C A C CPCTC Property 6

Statement Reason

1 is a right angle∠ DFE Given

2 is a right angle∠ DFG Given

3 =~∠ DFE ∠ DFG _________________ 1 2

4 co n gr i g

Given

5 1 Reflexive Property

6 =~DEF DGF _________________ 3 4 5

Line(s) Used


1 =~E F G F Given

2 =~∠ D E F ∠ H G F Given

3 =~∠ D F E ∠ H F G Vertical Angles Property

4 =~D E F H G F ASA Congruence Property 1 2 3


1 =~B C D C Given

2 =~∠ B A C ∠ D E C Given

3 =~∠ A C B ∠ E C D Vertical Angles Property

4 =~A B C E D C AAS Congruence Property 1 2 3

5 =~A B E D CPCTC Property 4


18.

19.

20.

21. (a)

(a) Adjust the figure on the right to explore the different triangles that can beformed. Then answer the question. Note that the figure will not be graded.



Reason: Choose one


(b) Adjust the figure on the right to explore the different triangles that can beformed. Then answer the question. Note that the figure will not be graded.



Reason: Angle-Side-Angle (ASA) Congruence Property


(a)

16 cm 16 cm

(b)


Yes No Yes No

(c) (d)


Yes No Yes No


1 Undefined UndefinedW Y Z W X Z Given

2 =~X Z Y Z Given

3 =~W Z W Z Reflexive Property

4 =~W Y Z W X Z HL Congruence Property 1 2 3

=m∠Q 75°© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 4 Pr ac t i ce T es t #1 / 15

21. (a)

(b)

22.

23.

24.

25.

=m∠Q 75°=m∠M 60°

=m∠V 61°=m∠W 58°=m∠X 61°


1 =~Q P Q R Given

2 bisectsQ S ∠ P Q R Given

3 =~∠ P Q S ∠ R Q S Definition of Angle Bisector 2

4 =~Q S Q S Reflexive Property

5 =~Q P S Q R S SAS Congruence Property 1 3 4

6 =~∠ P ∠ R CPCTC Property 5

T , +− f h g

Righttriangle

Not a righttriangle

Cannot bedetermined

, , D , 1 −2 E , −1 4 F , 5 6

, , J , −3 1 K , 1 7 L , 8 0

, , A , 4 11 B , 2 −12 C , −8 −4


Download - Chapter 4 Practice Test #1 - M2 Mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/... · 5 ECD=~ BCA SAS Congruence Property 1 3 4 Statement Reason Line(s) Used 1 EF GD Given 2∠EFD=~∠GDF

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