Free Printable Geometry Chapter 6

1.

A line, segment, or ray that divides an angle in half

a)

Perpendicular bisector

b)

Vertical angles

c)

Angle bisector

d)

Midsegment

2.

A line, segment, or ray that passes through the midpoint of a side and creates a 90 degree angle with that side.

a)

Perpendicular bisector

b)

Angle bisector

c)

Median

d)

Altitude

3.

Name the dashed segment:

a)

altitude

b)

angle bisector

c)

perpendicular bisector

d)

median

4.

Name the point of concurrency shown.

a)

Circumcenter

b)

Incenter

c)

Orthocenter

d)

Centroid

5.

What is the intersection of three perpendicular bisectors called?

a)

Circumcenter

b)

Incenter

c)

Orthocenter

d)

Centroid

6.

D is the circumcenter, find ED

a)

15

b)

16

c)

17

d)

19

7.

Which point is equidistant from the vertices?

a)

Circumcenter

b)

Incenter

c)

Orthocenter

d)

Centroid

8.

Find the measure of angle CAD.

a)

b)

c)

d)

9.

Find SV

a)

18

b)

36

c)

21

d)

9

10.

A perpendicular bisector bisects one side of a triangle.

a)

Always

b)

Sometimes

c)

Never

11.

An angle bisector bisects one side of a triangle.

a)

Always

b)

Sometimes

c)

Never

12.

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

a)

Always

b)

Sometimes

c)

Never

13.

16) Given that m∡RSQ = 58^o, RQ = 49, and TQ = 49 find m∡RST

a)

52^o

b)

58^o

c)

108^o

d)

116^o

14.

It divides or bisects a segment into two congruent segments; the point in the middle of the segment.

a)

point

b)

midpoint

c)

line

d)

bisector

15.

Which figure show M as the midpoint of line segment JK?

a)

b)

c)

16.

Find TM and MS given that M is the midpoint of the segment.

a)

TM = 15, MS = 15

b)

TM = 7.5, MS = 7.5

c)

TM = 7.5, MS = 15

d)

TM = 15, MS = 7.5

17.

Line l bisects the segment. Find the lengths of AN and AB.

a)

AN = 9.2, AB = 9.2

b)

AN = 9.2, AB = 18.4

c)

AN = 18.4, AB = 9.2

d)

AN = 18.4, AB = 18.4

18.

Line l bisects the segment. Find the value of x.

a)

x = 15

b)

x = 6

c)

x = 9

d)

x = 3

19.

A ray that divides an angle into two congruent adjacent angles.

a)

perpendicular bisector

b)

median

c)

angle bisector

d)

altitude

20.

Ray QS bisects <PQR. Find the measure of <SQR.

a)

m<SQR = 32.5

b)

m<SQR = 65

c)

m<SQR = 130

d)

m<SQR = 97.5

21.

Ray QS bisects <PQR. Find the measure of <PQS.

a)

m<PQS = 20

b)

m<PQS = 40

c)

m<PQS = 10

d)

m<PQS = 30

22.

Ray QS bisects <PQR. Find the measure of <RQS.

a)

m<RQS = 149

b)

m<RQS = 298

c)

m<RQS = 150

d)

m<RQS = 74.5

23.

<ABC is bisected by ray BD. Find the value of x.

a)

x = 76

b)

x = 75

c)

x = 73

d)

x = 25

24.

Find the measure of $\angle NJZ$

a)

38

b)

90

c)

52

d)

128

25.

Angle GHJ equals 52 degrees

a)

m∠GHK=26, m∠KHJ=26

b)

m∠GHK=26, m∠KHJ=52

c)

m∠GHK=52, m∠KHJ=52

d)

m∠GHK=52, m∠KHJ=26

26.

A line, segment, or ray that divides an angle in half

a)

Perpendicular bisector

b)

Altitude

c)

Angle bisector

d)

Median

27.

GT is a Median: find FE

a)

16

b)

32

c)

11

d)

26

28.

KL is a Median: Find LJ

a)

6

b)

12

c)

3

d)

9

29.

Which of the following describes a median of a triangle?

a)

A middle of the triangle.

b)

A segment with endpoints at the vertex and midpoint of the opposite side.

c)

A segment that connects two midpoints of two sides.

d)

A segment that connects the vertex and the opposite side at 90 degrees.

30.

Given segment AM is a median in ΔABC. Find the length of segment BC.

a)

34

b)

6

c)

17

d)

27

31.

The altitude is __________to the side of a triangle.

a)

parallel

b)

skew

c)

off

d)

perpendicular

32.

Name the segment/line/ray shown in the picture.

a)

Perpendicular Bisector

b)

Angle Bisector

c)

Median

d)

Altitude

33.

The figures above are examples of ...

a)

altitudes

b)

perpendicular bisectors

c)

medians

d)

angle bisectors

34.

10. What type of lines are shown?

a)

perpendicular bisectors

b)

medians

c)

altitudes

d)

angle bisectors

35.

13. Which line is an altitude?

a)

XY

b)

BY

c)

AZ

d)

XC

36.

A segment joining a vertex to the opposite side that is perpendicular to that side.

a)

perpendicular bisector

b)

angle bisector

c)

median

d)

altitude

37.

The ORTHOCENTER is the intersection of which special segments?

a)

Angle Bisectors

b)

Perpendicular Bisectors

c)

Medians

d)

Altitudes

38.

Segment BH is an example of which of the following?

a)

Perpendicular Bisector

b)

Altitude

c)

Median

d)

Midsegment

39.

If Z is the centroid, what type of segments are drawn?

a)

angle bisectors

b)

perpendicular bisectors

c)

altitudes

d)

medians

40.

Fill in the blank.
All three medians intersect at the point of concurrency called the ____________.

a)

Incenter

b)

Circumcenter

c)

Orthocenter

d)

Centroid

41.

What segment is parallel to EF?

a)

Segment PM

b)

Segment MN

c)

Segment NP

d)

Segment FG

42.

QR is a midsegment of triangle WUV. What is the length of segment QR?

a)

4

b)

8

c)

16

d)

32

43.

What is the measure of angle X?

a)

60

b)

40

c)

140

d)

100

44.

What is the measure of angle Y?

a)

60

b)

40

c)

140

d)

100

45.

QR is a midsegment of triangle WXY. What is the length of segment WY?

a)

3

b)

6

c)

9

d)

12

46.

QR is a midsegment of triangle FGH. Solve for the value of x?

a)

5.5

b)

11

c)

-5.5

d)

-11

47.

QR is a midsegment of triangle BCD. Solve for the value of x.

a)

11

b)

18

c)

9

d)

-7

48.

TS is a midsegment of triangle GHI. Solve for the value of x.

a)

4

b)

6

c)

8

d)

10

49.

KJ is a midsegment of WXV. What is the length of segment VX?

a)

6

b)

12

c)

9

d)

-2

50.

IJ is a midsegment of triangle MLN. What is the length of segment IJ?

a)

9

b)

6

c)

18

d)

0

51.

Is DE 1/2 the length of BC?

a)

Yes

b)

No

c)

Sometimes

52.

Name a midsegment of ⌂ABC

a)

segment AC

b)

segment DE

c)

segment AB

d)

segment BC

53.

Name a segment that has the same length as segment BD

a)

segment BE

b)

segment DE

c)

segment AD

d)

segment AC

54.

Name a segment that is half the length of segment AC

a)

segment AD

b)

segment BE

c)

segment DE

d)

segment BC

55.

Can the following side measures form a triangle?
3, 5, 8

a)

Yes

b)

No

56.

9. Which of these lengths CANNOT represent the sides of a triangle?

a)

32, 34, 60

b)

28, 30, 58

c)

13, 20, 27

d)

2, 4, 5

57.

Which of the following does not represent the lengths of the sides of a triangle?

a)

2 cm, 6 cm, 7 cm

b)

5 cm, 2 cm, 5 cm

c)

5 cm, 5 cm, 8 cm

d)

3 cm, 10 cm, 15 cm

58.

Select the measurements that match the sides of a triangle.

a)

7, 9, 19

b)

7, 12, 1

c)

7, 7, 7

d)

7, 7, 16

59.

If the longest side of the triangle was 10. Then the two shorter sides must have a sum that is ....?

a)

any length

b)

equal to 10

c)

greater than 10

d)

less than 10

60.

Will these three sides form a triangle?

a)

yes

b)

no

c)

sometimes

61.

Will these line segments form a triangle?

a)

yes

b)

no

c)

sometimes

62.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

a)

more than 6 but less than 20

b)

more than 20 but less than 6

c)

less than 6 but more than 20

63.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 mm, 4 mm

a)

more than 3 but less than 11

b)

more than 11 but less than 3

c)

less than 3 but more than 11

64.

What assumption would you make to start the indirect proof of ∆ABC≅∆DEF?

a)

∆ABC≠∆DEF

b)

∆ABC≇∆DEF

c)

<ABC≠<DEF

d)

AB≅DE

65.

What assumption would you make to start the indirect proof of AB≅BC?

a)

AB≠BC

b)

BA≅CB

c)

B is the midpoint of AC

d)

B is the perpendicular bisector to AC

66.

What assumption would you make to start the indirect proof of:

"There can be only one 90 angle in a triangle."

a)

There can be more than one 90 angle in a triangle.

b)

<a+<b+<c=180

c)

<a+<b+<c≠180

d)

all the angles in a triangle add up to 180.

67.

Which statement is a contradiction of the statement XY≅RT?

a)

XY<RT

b)

TR≅YX

c)

XY≈RT

d)

XY≤RT

68.

Compare m∠TUW and m∠VUW

a)

m∠TUW < m∠VUW

b)

m∠TUW > m∠VUW

c)

m∠TUW = m∠VUW

69.

Compare PS and SR.

a)

PS < SR

b)

PS > SR

c)

PS = SR

70.

Find the range of possible values for x.

a)

2 < x < 6

b)

x < 6

c)

x < 2

d)

x > 6

71.

Compare $m\angle ACD\ and\ m\angle GDE$

a)

$m\angle ACB\ >\ m\angle GDE$

b)

$m\angle ACD\ <\ m\angle GDE$

c)

$m\angle ACB\ =\ m\angle GDE$

d)

$\angle ACB\ \cong\ \angle GDE$

72.

Compare QT and ST

a)

$QT\ <\ ST$

b)

$QT\ >\ ST$

c)

$QT\ =\ ST$

d)

$\overline{QT}\ \cong\ \overline{ST}$

73.

Find the range of possible values for x.

a)

$\frac{7}{2}<x<24$

b)

$x<6$

c)

$24<x$

d)

$\frac{11}{2}<x<6$

74.

Which of the following is a possible length for segment AC

a)

10

b)

15

c)

17

d)

9

75.

Select the correct answer

a)

A

b)

B

c)

C

d)

D

76.

Select the correct answer

a)

A

b)

B

c)

C

d)

D

77.

Which of the following statements must be true?

a)

RS > XY

b)

RS < XY

c)

ST < XZ

d)

$\angle T\ >\angle Z$

78.

What are the possible values for x?

a)

x < 16

b)

4 < x < 16

c)

x < 40

d)

4 < x < 40

79.

Using the hinge theorem, we can say that Angle 1 _____ Angle 2.

a)

Less than

b)

Greater than

c)

Equal to

d)

Half of

80.

Compare measure of angle Y and measure of angle M.

a)

measure of angle Y = measure of angle M

b)

measure of angle Y > measure of angle M

c)

measure of angle Y < measure of angle M

d)

Not enough information is given.

Geometry Chapter 6

Total questions: 80

Worksheet time: 1hrs 20mins

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