Free Printable Geo Hon Unit 6 Summative Review

1.

Define: CIRCUMCENTER OF A TRAINGLE

a)

the intersection point of the three perpendicular bisectors of a triangle

b)

when a circle passes through the three vertices of a triangle

c)

the point of intersection of three or more lines

d)

the intersection point of the three angle bisectors of a triangle

2.

Define: INCENTER OF A TRIANGLE

a)

the intersection point of the three angle bisectors of a triangle

b)

when three or more lines intersect at a single point

c)

the intersection point of the three perpendicular bisectors of a triangle

d)

the point of intersection of three or more lines

3.

Which of the images represents the Circumcenter of a Triangle

a)

First

b)

Second

c)

Third

4.

Which of the images represents the Incenter of a Triangle

a)

First

b)

Second

c)

Third

5.

Name the point of concurrency shown.

a)

Circumcenter

b)

Incenter

c)

neither

d)

Pokecenter

6.

The figure is an example of a(n) ...

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

7.

Which of the following points is the BALANCE POINT of a triangle. The correct method is shown in the triangle if you look at the markings.

a)

A. Circumcenter

b)

B. Orthocenter

c)

C. Centroid

d)

D. Midpoint

8.

The centroid cuts each median into two segments. The shorter segment is ___________ the length of the entire median.

a)

one third

b)

two thirds

c)

three fourths

d)

one half

9.

The centroid is the intersection point of the three ____ of a triangle.

a)

Medians

b)

Midsegments

c)

Perpendicular Bisectors

d)

Angle Bisectors

10.

The figure is an example of a(n) ...

a)

angle bisector

b)

midsegment

c)

altitude

d)

median

11.

Which center points of a triangle are always inside the triangle?

a)

Centroid and Circumcenter

b)

Orthocenter and Incenter

c)

Incenter and Centroid

d)

Circumcenter and Incenter

12.

The three altitudes of a triangle intersect at the?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

13.

If G is the centroid of triangle ABC and GF= 4. Find the length of GC.

a)

4

b)

8

c)

12

d)

Not Enough Information

14.

Write an inequality showing the possible 3rd side of a triangle. 5 & 15

a)

5<x<15

b)

10<x<20

c)

15<x<5

d)

20<x<10

15.

Write an inequality for the possible 3rd side of a triangle. 25 & 35

a)

25<x<35

b)

35<x<25

c)

10<x<60

d)

60<x<10

16.

Using hinge theorem which side is bigger?

a)

AR

b)

RB

c)

AC

d)

CR

17.

It is called the HINGE theorem, because...

a)

the vertex of the angle acts like a hinge to open the triangle.

b)

it's named after Joseph Hinge, the man who discovered it.

c)

"hinge" is the Spanish word for angle.

d)

the triangle makes a hinge shape, like a tent.

18.

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)

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

19.

Compare QT and ST

a)

$QT\ <\ ST$

b)

$QT\ >\ ST$

c)

$QT\ =\ ST$

d)

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

20.

Find the range of possible values for x.

a)

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

b)

$x<6$

c)

$24<x$

d)

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

21.

Find the range of possible values of x.

a)

$\frac{5}{3}<x<8$

b)

$-\frac{3}{2}<x>8$

c)

$\frac{32}{3}<x<27$

d)

$27<x<37$

22.

Which inequality relates $\angle FBG\ and\ \angle BFA$ ?

a)

$m\angle FBG\ <m\angle BFA$

b)

$m\angle FBG\ >m\angle BFA$

c)

$m\angle FBG\ \ge m\angle BFA$

d)

$m\angle FBG\ \le m\angle BFA$

23.

What is the "statement" for step 3 of the proof?

a)

AD=DA

b)

AN = AH

c)

HD=ND

d)

HD=DN

24.

Two sides of each triangle in the circle are formed
from the radii of the circle. Compare EF and FG.

a)

EF = FG

b)

EF < FG

c)

EF > FG

d)

Not enough information is given.

25.

Find the value of x by using the exterior angle theorem.

a)

A

b)

B

c)

C

d)

D

26.

Select all that are TRUE.

a)

AB > AE

b)

BE > CE

c)

BE > CD

d)

CD < DE

e)

CE > BC

27.

In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.
Find the length of YZ.

a)

30

b)

15

c)

5

d)

7.5

28.

In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.
If XP = 8, then PC = _______

a)

2.7

b)

12

c)

5

d)

4

29.

In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.
If PB = 3, then YB = _______

a)

6

b)

9

c)

1.5

d)

3

30.

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

a)

Perpendicular Bisector

b)

Angle Bisector

c)

Median

d)

Altitude

31.

Which of the following is a true statement based on this diagram? Select all that apply.

a)

P is equidistant from A, B, and C

b)

ABC is an Isosceles triangle

c)

APC is an Isosceles triangle

d)

AB = AC

32.

Use the figure to determine which of the following angles has the greatest measure: $\angle\ 1,\ \angle\ 3,\ \angle4$

a)

$\angle1$

b)

$\angle3$

c)

$\angle4$

d)

Not enough information

33.

Use the figure to determine which of the following angles has the greatest measure: $\angle\ 4,\ \angle\ 8,\ \angle9$

a)

$\angle4$

b)

$\angle8$

c)

$\angle9$

d)

Not enough information

34.

SPORTS The figure shows the position of three trees on one part of a disc golf course. At which tree position is the angle between the trees the greatest?

a)

Tree 1

b)

Tree 2

c)

Tree 3

35.

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are less than $\angle1$

a)

$\angle3,\ \angle4,\ \angle5,\ \angle7,\ \angle8$

b)

$\angle3,\ \angle4,\ \angle5,\ \angle6,\ \angle8$

c)

$\angle2,\ \angle6,\ \angle7,\ \angle8$

d)

$\angle2,\ \angle6,\ \angle8,\ \angle9$

36.

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are less than $\angle3$

a)

$\angle2,\ \angle6,\ \angle8,\ \angle9$

b)

$\angle1,\ \angle6,\ \angle8$

c)

$\angle5,\ \angle7,\ \angle8$

d)

$\angle2,\ \angle4,\ \angle7,\ \angle8$

37.

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

38.

Identify the shortest side measure.

a)

QP

b)

QM

c)

MP

39.

List the side measures in order, shortest to longest.

a)

QM, QP, MP

b)

MQ, MP, QP

c)

MP, MQ, QP

40.

List the angles in order by measure, smallest to largest.

a)

∠B, ∠A, ∠C

b)

∠A∠,B, ∠C

c)

∠A, ∠C, ∠B

41.

What theorem states that in any triangle if you take any 2 sides of the triangle, their sum must be greater than the length of the 3rd side?

a)

Triangle Inequality Theorem

b)

Corollary to the triangle exterior angle theorem

c)

Triangle exterior angle theorem

d)

SAS inequality theorem

42.

Which is the hinge theorem?

a)

If 2 sides of a triangle are congruent to 2 sides of another triangle and the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle, then the included angle in the 1st triangle is greater than the included angle in the 2nd triangle.

b)

If 2 sides of one triangle are congruent to 2 sides of another triangle and the included angle (angle between the 2 sides) of the 1st triangle is larger than the included angle of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle.

43.

Which is the converse of the hinge theorem

a)

If 2 sides of one triangle are congruent to 2 sides of another triangle and the included angle (angle between the 2 sides) of the 1st triangle is larger than the included angle of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle.

b)

If 2 sides of a triangle are congruent to 2 sides of another triangle and the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle, then the included angle in the 1st triangle is greater than the included angle in the 2nd triangle.

44.

Select the correct answer

a)

A

b)

B

c)

C

d)

D

45.

Select the correct answer

a)

A

b)

B

c)

C

d)

D

46.

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

a)

Less than

b)

Greater than

c)

Equal to

d)

Half of

47.

Find the shortest segment in △PQS.

a)

QS

b)

PQ

c)

PS

d)

Cannot Determine

48.

Find the longest segment in △QRS

a)

QR

b)

RS

c)

QS

d)

Cannot Determine

49.

Find the angle with the smallest measure in △VUW.

a)

Angle UVW

b)

Angle UWV

c)

Angle WUX

d)

Angle VUW

50.

Find the angle with the greatest measure in △UWX

a)

Angle UWX

b)

Angle WUX

c)

Angle X

d)

Angle V

51.

Write an inequality about the length of GH.

a)

GH > 9

b)

GH < 7

c)

GH > 7

d)

GH < 6

52.

Given: AB = DE, and BE > AD

Prove: m∠CAE > m∠CEA

Which 2 steps would be need to prove this?

a)

SSS, Hinge Theorem

b)

Reflexive Prop., Converse of Hinge Theorem

c)

ASA, Converse of Hinge Theorem

d)

Reflexive Prop, Hinge Theorem

53.

Find the range of possible values for x

a)

$x>7$

b)

$-\frac{17}{3}<x>7$

c)

$-\frac{17}{3}<x<7$

d)

$x<7$

54.

The three perpendicular bisectors of a triangle intersect at the?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

55.

The three altitudes of a triangle intersect at the?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

56.

The three angle bisectors of a triangle intersect at the?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

57.

The three medians of a triangle intersect at?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

58.

Which point of concurrency is equidistant from every side?

a)

Circumcenter

b)

Centroid

c)

Orthocenter

d)

Incenter

59.

Which point of concurrency is equidistant from every vertex?

a)

Centroid

b)

Circumcenter

c)

Orthocenter

d)

Incenter

60.

Which point of concurrency is always the midpoint of the hypotenuse in a right triangle?

a)

Circumcenter

b)

Orthocenter

c)

Centroid

d)

Incenter

Geo Hon Unit 6 Summative Review

Total questions: 60

Worksheet time: 2hrs 38mins

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