Free Printable Geometry Unit 5 Review: Triangle Relationships

1.

The first step of an indirect proof is to ____?

a)

write the given

b)

assume the negation (opposite) of the given

c)

assume the negation (opposite) of what you are trying to prove

d)

contradict the given

2.

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

a)

angle bisector

b)

midsegment

c)

altitude

d)

median

3.

The centroid is the point of concurrency of the 3 ____ of a triangle.

a)

Medians

b)

Midsegments

c)

Perpendicular Bisectors

d)

Angle Bisectos

4.

The altitudes of a triangle intersect at the _________________________.

a)

Centriod

b)

Circumcenter

c)

Incenter

d)

Orthocenter

5.

Which of the following describes a median of a triangle?

a)

A. A middle of the triangle.

b)

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

c)

C. A segment that connects two midpoints of two sides.

d)

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

6.

Find the length of AD

a)

2

b)

4

c)

6

d)

8

7.

Which of the following segments represents an altitude?

a)

BX

b)

AZ

c)

AC

d)

BZ

8.

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

a)

angle bisector

b)

perpendicular bisector

c)

median

d)

midsegment

9.

Identify the type of segment pictured below.

a)

Median

b)

Midsegment

c)

Altitude

d)

Perpendicular Bisector

e)

Angle Bisector

10.

CF, BE, and AD are the medians of the triangle. If BF =10, find AF.

a)

20

b)

10

c)

5

d)

Not Enough Information

11.

Fill in the blank:

A perpendicular bisector is perpendicular to and passing through the ___________________ of a segment.

a)

endpoint

b)

corner

c)

midpoint

d)

side

12.

What assumption would you make to prove the following statement by indirect proof:

x > 2?

a)

x ≤ 2

b)

x < 2

c)

x > 2

d)

x = 2

13.

What is the length of DC

a)

4

b)

1

c)

2

d)

3

14.

A segment from a vertice to the midpoint on the opposite side

a)

median

b)

midsegment

c)

altitude

d)

angle bisector

15.

The centroid of a triangle is ___________ inside a triangle.

a)

always

b)

never

c)

sometimes

16.

Find the measure of QM

a)

5

b)

12

c)

10

d)

6

17.

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

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

18.

Can the following lengths be made into a triangle? 2cm, 4cm, 7cm

a)

yes, because 2+4 <7

b)

yes, because

2+4>7

c)

no, because

2+4<7

d)

no, because

2+4>7

19.

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

a)

34

b)

6

c)

17

d)

27

20.

State the assumption you would make to prove the following statement by indirect proof:

\overline{AB}\cong\overline{CD}

a)

undefined

b)

$\overline{AB}$ ≇ $\overline{BC}$

c)

B is the midpoint of AB

d)

AB is the perpendicular bisector of CD

21.

The circumcenter of a triangle is ____________ inside the triangle.

a)

always

b)

never

c)

sometimes

22.

Segments CF, AD, and BE are medians of triangle ABC. If BE=15x and BG=8x+14, find x.

a)

7

b)

2

c)

4

d)

5

23.

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

a)

one third

b)

two thirds

c)

three fourths

d)

one half

24.

The incenter of a triangle is ___________ inside the triangle.

a)

always

b)

never

c)

sometimes

25.

Given the following diagram, solve for (6pts):

X=_________

<WXZ=______

<WXY=______

4 lines

26.

Find the centroid of triangle whose vertices are (1, 10) (-7, 2) and (-3, 7).

a)

(-3, 6.3)

b)

(6.3, -3)

c)

(3, 6.3)

d)

(-3, -6.3)

27.

What is the measure of PR?

a)

5.4

b)

6

c)

19.8

d)

22.5

28.

1. The ___________ ______________ Theorem says that any point on an angle bisector will be equidistant to the sides of the angle.

a)

Perpendicular Bisector

b)

Triangle Inequalities

c)

Circumcenter

d)

Angle Bisector

29.

If G is the centroid of triangle ABC and AG= 16. Find the length of GD.

a)

8

b)

16

c)

24

d)

Not Enough Information

30.

If TP=27, ZP=?

a)

18

b)

9

c)

13.5

d)

54

31.

The ____________ of the Perpendicular Bisector Theorem states that if a point is equidistant to the endpoints of a segment, then that point lies on the perpendicular bisector.

a)

Bisector

b)

Congruence

c)

Converse

d)

Concurrent

32.

The orthocenter of a triangle is __________ inside a triangle.

a)

always

b)

never

c)

sometimes

33.

Solve for y:

a)

4

b)

7

c)

14

d)

20

34.

Name the angles of the triangle in order from smallest to largest:

a)

<R, <K, <J

b)

<K, <J, <R

c)

<K, <R, <J

d)

<J, <K. <R

35.

In ΔABC, if m∠ABF = 39° and BF is an angle bisector, find m∠BCE.

a)

90 degrees

b)

45 degrees

c)

39 degrees

d)

51 degrees

e)

12 degrees

36.

Name the sides of the triangle, longest to shortest:

a)

XZ, YZ, XY

b)

YZ, XY, XZ

c)

XY, YZ, XZ

d)

XZ, XY, YZ

37.

Can the following lengths be made into a triangle? 3cm, 5cm, 7cm

a)

yes, because

3+5<7

b)

yes, because

3+5>7

c)

no, because

3+5<7

d)

no, because

3+5>8

38.

Identify an altitude of ΔABC.

a)

CE

b)

GH

c)

BF

d)

AD

e)

CB

39.

The altitudes of a triangle insect of the _________________________.

a)

Centriod

b)

Circumcenter

c)

Incenter

d)

Orthocenter

40.

Identify a median of ΔABC

a)

BF

b)

GH

c)

AD

d)

CE

e)

none of these

41.

An indirect proof is also called proof by __________________.

a)

Direct reasoning

b)

Opposition

c)

Contradiction

d)

Assumption

Geometry Unit 5 Review: Triangle Relationships

Total questions: 41

Worksheet time: 24mins

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