Chapter 6 Practice Exam

Problems and answers to the practice exam as well as what

section they came from so you can study!

1. What is the sum of the angle measures of a 35-gon?

A. 5940B. 6660C. 6120D. 6300

59406660

61206300

19%

38%

19%

24%

1. What is the sum of the angle measures of a 35-gon?

Correct Answer is A. 59406-1

2. Find the missing values of the variables. The diagram is not to scale.

A. B. C. D.

𝑥=74;𝑦=103

𝑥=74;𝑦=93

𝑥=93;𝑦=74

𝑥=103;𝑦=119

10% 10%

52%

29%

x°y°106° 74°

119°

2. Find the missing values of the variables. The diagram is not to scale.

x°y°106° 74°

119°

Correct answer is C. 6-1

3. How many sides does a regular polygon have if each exterior angle

measures 30?

A. 15 sidesB. 12 sidesC. 14 sidesD. 11 sides

15 sides

12 sides

14 sides

11 sides

24%

14%

0%

62%

3. How many sides does a regular polygon have if each exterior angle

measures 30?

Correct answer is B. 12 sides

6-1

x°y°

z°

9631

4. Find the values of the variables in the parallelogram. The diagram is not to scale.

A. B. C. D.

𝑥=53, 𝑦=31,

𝑧=96

𝑥=53, 𝑦=53,

𝑧=127

𝑥=31, 𝑦=53,

𝑧=96

𝑥=31, 𝑦=53,

𝑧=127

19%10%

67%

5%

x°y°

z°

9631

4. Find the values of the variables in the parallelogram. The diagram is not to scale.

Correct answer is C. 6-2

5. Find AM in the parallelogram if PN =15 and AO = 6. The diagram is not to scale.

A. 12B. 6C. 15D. 7.5

12 6 15 7.5

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38%

5%

38%

M N

P O

A

5. Find AM in the parallelogram if PN =15 and AO = 6. The diagram is not to scale.

M N

P O

A

The diagonals of a parallelogram bisect each other

If AO = 6 then AM = 6.

Correct answer is B. 6 6-2

6. LMNO is a parallelogram. If NM = x + 5 and OL = 2x + 3, find the value of x and then find NM and OL.

A. B. 7C. D.

𝑥=4, 𝑁𝑀=9, 𝑂𝐿=9

𝑥=2, 𝑁𝑀=7, 𝑂𝐿=7

𝑥=2, 𝑁𝑀=9, 𝑂𝐿=7

𝑥=4, 𝑁𝑀=7, 𝑂𝐿=9

10% 10%19%

62%

O N

L M

6. LMNO is a parallelogram. If NM = x + 5 and OL = 2x + 3, find the value of x

and then find NM and OL.O N

L MOpposite sides of a parallelogram are congruent so NM = OL.

Correct answer is B. 7 6-2

7. In the figure, the horizontal lines are parallel and Find JM. The diagram is

not to scale.

A. 27B. 36C. 9D. 18

27 36 9 18

48%

10%5%

38%

9

M A

L B

K C

J D

Since the lines are parallel and equidistant, The distance from .Correct answer is A. 27 6-2

7. In the figure, the horizontal lines are parallel and Find JM. The diagram is not

to scale.

9

M A

L B

K C

J D

8. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.

and

A. Yes; opposite sides are congruent.B. Yes; two opposite sides are both parallel and

congruent.C. Yes; diagonals of a parallelogram bisect each

other.D. No; you cannot determine that the quadrilateral

is a parallelogram.

Yes; opposit

e sides a

re c...

Yes; tw

o opposite si

des a..

Yes; diagonals

of a para

ll...

No; you ca

nnot determ

i..

14% 14%

43%

29%

X

ZW

Y

N

8. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.

and X

ZW

Y

N

Since you are given that the diagonals bisect each other yes the quad is a parallelogram.

Correct answer is C. Yes; diagonals of a parallelogram bisect each other. 6-3

9. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.

A. B. C. D. 𝑥=8, 𝑦=6

𝑥=6, 𝑦=8

𝑥=8, 𝑦=17

𝑥=8, 𝑦=10

48%

10%

19%24%

A

CD

B

3x – 14

x + 2

4y – 7

y + 11

9. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.

A

CD

B

3x – 14

x + 2

4y – 7

y + 11

Correct answer is A. 6-3

10. Based on the information in the diagram, can you prove that the figure is a

parallelogram? Explain.

A. Yes; the diagonals bisect each other.

B. No; you cannot prove that the quadrilateral is a parallelogram.

C. Yes; two opposite sides are both parallel and congruent.

D. Yes; the diagonals are congruent.

Yes; th

e diagonals bise

ct ...

No; you ca

nnot pro

ve tha...

Yes; tw

o opposite si

des a..

Yes; th

e diagonals are

c...

33%

24%29%

14%

10. Based on the information in the diagram, can you prove that the figure is a

parallelogram? Explain.

Yes because the diagonals bisect each other the figure will be a parallelogram.

Correct answer is A. Yes; the diagonals bisect each other.

6-3

A. B. C. D.

𝑚∠2=40, 𝑚∠3=70

𝑚∠2=140, 𝑚∠3=20

𝑚∠2=40, 𝑚∠3=20

𝑚∠2=140, 𝑚∠3=70

10%19%

5%

67%

11. In the rhombus, What are and ? The diagram is not to scale.

3

2

1 ||

||

11. In the rhombus, What are and ? The diagram is not to scale.

3

2

1 ||

||

Since it is a rhombus opposite angles are congruent so

And a rhombus has diagonals that bisect the opposite angles therefore

Correct answer is B. . 6-4

12. Which description does NOT guarantee that a quadrilateral is a square?

A. has all sides congruent and all angles congruent

B. is a parallelogram with perpendicular diagonals

C. has all right angles and has all sides congruent

D. is both a rectangle and a rhombus

has all s

ides congru

ent a..

is a paral

lelogram with

...

has all r

ight angles a

nd h..

is both

a recta

ngle and ...

19%24%

14%

43%

12. Which description does NOT guarantee that a quadrilateral is a square?

-has all sides congruent and all angles congruent must be both rhombus and rectangle so square-has all right angles and has all sides congruentmust be both rectangle and rhombus so square-is both a rectangle and a rhombusTherefore it is a square equal sides and all right angles.

BUT B. is a parallelogram with perpendicular diagonalsA rhombus has perpendicular diagonals but it does not have to be square, there fore the correct answer is B.6-4

13. DEFG is a rectangle. DF = 5x – 3 and

EG = x + 5. Find the value of x and the length of each diagonal.

A. B. C. D.

𝑥=1, 𝐷𝐹=6, 𝐸𝐺=6

𝑥=2, 𝐷𝐹=7, 𝐸𝐺=12

𝑥=2, 𝐷𝐹=6, 𝐸𝐺=6

𝑥=2, 𝐷𝐹=7, 𝐸𝐺=7

5%

57%

19%19%

13. DEFG is a rectangle. DF = 5x – 3 and

EG = x + 5. Find the value of x and the length of each diagonal.

Correct answer is D.

6-4

14. Which statement is true?

A. All squares are rectangles.B. All quadrilaterals are rectangles.C. All parallelograms are rectangles.D. All rectangles are squares.

All squares a

re re

ctangles.

All quadrila

teral

s are

rec..

.

All paralle

lograms a

re re...

All recta

ngles a

re sq

uares.

38%

29%24%

10%

14. Which statement is true?-All quadrilaterals are rectangles.Not true could be a rhombus, kite, etc.

-All parallelograms are rectangles.Not true could be a rhombus.

-All rectangles are squares.Not true some do not have all sides congruent.

• All squares are rectangles.This statement is always true to be a square it must have 4 right angles which makes it a rectangle.

Correct answer is A. All squares are rectangles. 6-4

15. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.

A. Parallelogram ABCD is a rectangle, because the diagonal creates congruent angles.

B. Parallelogram ABCD is a square, because all four angles have the same measure.

C. Parallelogram ABCD is a rhombus, because the diagonal bisects two angles.

D. There is not enough information.

Paralle

logram ABCD is

a ...

Paralle

logram ABCD is

a ...

Paralle

logram ABCD is

a...

There is not e

nough inf..

.

14%19%

62%

5%

66º66º66º 66º

15. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. 66º66º

66º 66º

-Parallelogram ABCD is a rectangle, because the diagonal creates congruent angles.Not true rectangles do not bisect the opposite angles.

-Parallelogram ABCD is a square, because all four angles have the same measure.Not square 66 + 66 is not a right angle.

-Parallelogram ABCD is a rhombus, because the diagonal bisects two angles.YES a rhombus does bisect the opposite angles.Correct answer is C. 6-5

16. In quadrilateral ABCD, and For what value of x is ABCD a rectangle?

A. 18B. 12C. 16D. 14

18 12 16 14

10%5%

14%

71%

A

CD

B

E

16. In quadrilateral ABCD, and For what value of x is ABCD a rectangle?

A

CD

B

E

Correct answer is B. 12 6-5

17. In quadrilateral ABCD, and For what value of x is ABCD a rhombus?

A. 3B. 4C. 5D. 6

3 4 5 6

19%

0%

29%

52%

A

CD

B

17. In quadrilateral ABCD, and For what value of x is ABCD a rhombus?A

CD

B

To be a rhombus the diagonals must bisect the opposite angles.

The correct answer is B. 4. 6-5

18.

A.1B. 154C. 77D.26

1154 77 26

0%

33%

67%

0%

18.

Base angles of an isosceles trapezoid are congruent.

Plugging back into the equations we see the following:

However the question asked for angle K which is supplementary

Correct answer then is B. 154.6-6

19. Find and in the kite. The diagram is not to scale.

A. B. C. D.

𝑚∠1=17, 𝑚∠3=73

𝑚∠1=17, 𝑚∠3=17

𝑚∠1=73, 𝑚∠3=17

𝑚∠1=73, 𝑚∠3=73

100%

0%0%0%

1

2317°

D B

A

C

19. Find and in the kite. The diagram is not to scale.

1

2317°

D B

A

C

The measure of angle 1 is the same as 17 since they are corresponding parts in congruent

triangles.

Angle three can be found using the triangle.

Correct answer is A.

6-6

20. Find the values of the variables and the lengths of the sides of this kite.

A. B. C. D.

𝑥=9, 𝑦=14;11,

20

𝑥=14, 𝑦=9;11,

11

𝑥=14, 𝑦=9;6, 1

6

𝑥=9, 𝑦=14;6, 1

6

0%

100%

0%0%

||

| | ||

y – 3 x + 2

2x + 2 x + 11

20. Find the values of the variables and the lengths of the sides of

this kite.

||

| | ||

y – 3 x + 2

2x + 2 x + 11

The top two sides are congruent and the bottom two sides are congruent so for ease solve the bottom two first they both have x.

Plugging into the top equations you get:

Plugging into the bottom equations:

Correct answer is A. 6-6

Chapter 6 Exam

• We will test tomorrow Journals will be due at the end of the test.

• Go over exams on Thursday.• RETEST Friday• Portfolios due on Monday!