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Geometry: Ch5-Relationships in Triangles

Total questions: 46

Worksheet time: 7hrs 50mins

Name
Class
Date
1.
Find HG
a)
28
b)
14
c)
41
d)
7
2.
Find PQ
a)
10
b)
3
c)
-2
d)
5
3.
Find AD AND BC
a)
5;12
b)
16;4
c)
12; 16
d)
5;16
4.
What is the length of DC
a)
4
b)
1
c)
2
d)
3
5.
Find x, then the measure of AC
a)
x=2, AC=8
b)
x=2, AC=16
c)
x=4, AC=8
d)
x=4, AC=16
6.
Find x, then the measure of AC
a)
x=2, AC=8
b)
x=2, AC=16
c)
x=4, AC=8
d)
x=4, AC=16
7.
This triangle has...
a)
Altitudes
b)
Perpendicular Bisectors 
c)
Midsegments
d)
Medians
8.

Based on the markings, which segment represents a perpendicular bisector?

a)

Segment BA

b)

Segment CF

c)

Segment DE

d)

segment BG

9.
Which of the following describes a perpendicular bisector of a triangle?
a)
A segment that is perpendicular to the side of a triangle at its midpoint.
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. 
10.

The CIRCUMCENTER is the intersection of which special segments?

a)

Angle Bisectors

b)

Perpendicular Bisectors

c)

Medians

d)

Altitudes

11.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

12.

The circumcenter and orthocenter can be outside the triangle if the triangle is ...

a)

obtuse

b)

acute

c)

iscolese

d)

right

13.

If AF = 10x-3, and FC = 8x+3, what is AC?

a)

3

b)

6

c)

27

d)

54

14.

If BC is 18, what is DC?

a)

6

b)

9

c)

12

d)

18

15.

[Perpendicular Bisectors and Circumcenter]

If GC is 11, what is AG?

a)

11

b)

9

c)

cannot determine

d)

5.5

16.

[Perpendicular Bisectors and Circumcenter]

If CG = 4x+3 and AG = 3x+4, what is BG?

a)

14

b)

3

c)

7

d)

3.5

17.
A line, segment, or ray that passes through the midpoint of a side that is creates a 90 degree angle with that side.
a)
Perpendicular bisector
b)
Angle bisector
c)
Median
d)
Altitude
18.

Which term best describes line segment TV?

?

a)

Median

b)

Altitude

c)

Perpendicular Bisector

d)

Angle Bisector

19.

∠IHJ is a right angle

Which term describes line segment JH??

a)

Median

b)

Altitude

c)

Perpendicular Bisector

d)

Angle Bisector

20.

Which line segment is an altitude of △SUW??

a)

SV

b)

WT

c)

SU

d)

SW

21.

Which line segment is a median of △PQS??

a)

SQ

b)

PQ

c)

PR

d)

TQ

22.

Which line segment is an angle bisector?

a)

AB

b)

AD

c)

EB

d)

AC

23.

Which line segment is an angle bisector?

a)

CA

b)

EB

c)

DE

d)

DB

24.

Which line segment is a median of △DEG?

a)

GE

b)

GD

c)

DF

d)

EH

25.

Which line segment is an altitude of △PRT?

a)

SU

b)

TQ

c)

TP

d)

ST

26.

An angle is bisected, forming two new angles. Each new angle has a measure of 15°. What was the measure of the original angle? (enter number only)

(a)  

27.

After bisecting an angle, Eric has two new angles, each with a measure of 19°. What was the measure of the original angle? (number only)

(a)  

28.

Given the segment BP bisects ∠CBD Find m∠2 if m∠2 = 7x + 5 and m∠1 = 9x − 5.

FIND m∠2= (a)   degrees

29.

The figure shows a triangle with one of its angle bisectors. Find x if m∠2 = 4x + 5 and m∠1 = 5x − 2.

a)

x = 7

b)

x = 3

c)

x = -7

d)

x = 1/3

30.

What is the length of segment DE?

(a)  

31.

What is m∠HIJ? (number only)

(a)  

32.
Write the equation of the perpendicular bisector of the line AB given:
A(3,-3) & B(1,-1)
a)
y = x - 4
b)
y = x + 4
c)
y = 1/2x -4
d)
y = x + 2
33.
What is the midpoint between (-4,4) and (-2,2)?
a)
(3,2)
b)
(-3,3)
c)
(4,5)
d)
(6,7)
34.
What is the midpoint between (3, -1) and (7, -5)
a)
(5, -2)
b)
(10, -6)
c)
(5, -3)
d)
(2, -2)
35.

m=2/3

Which slope is Perpendicular?

a)

m=3

b)

m=-3/2

c)

m=2/3

d)

m=-3

36.
Slopes of perpendicular lines are...
a)
opposite reciprocals.
b)
opposites.
c)
identical.
d)
always 7.
37.
Write the equation of the perpendicular bisector of the line AB given:
A(1,3) & B(-3,5)
a)
y = 2x + 4
b)
y = 2x + 6
c)
y = -2x + 6
d)
y = 2x - 6
38.
The centroid is the point of concurrency of the 3 ____ of a triangle. 
a)
Medians
b)
Midsegments
c)
Perpendicular Bisectors
d)
Angle Bisectos
39.
If Z is the centroid, what type of segments are drawn?
a)
angle bisectors
b)
perpendicular bisectors
c)
altitudes
d)
medians
40.
If DL = 24, then DG = 
a)
16
b)
8
c)
12
d)
36
41.
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
42.

Is segment AB a median, altitude, neither or both?

a)

median

b)

altitude

c)

neither

d)

both

43.
[Medians and Centroid]
If AC = 16, what is AM?
a)
4
b)
8
c)
6
d)
10
44.
The altitudes of a triangle intersect at the _________________________.
a)
Centriod
b)
Circumcenter
c)
Incenter
d)
Orthocenter
45.
Find the measure of the indicated angle. 
a)
34
b)
46
c)
62
d)
36
46.

 In the isosceles triangle QRSQRS  ,  RT‾\overline{RT}  is the angle bisector of  ∠QRS\angle QRS . You want to prove the base angles of this triangle are congruent. You start by stating  ∠1≅∠2\angle1\cong\angle2  . What is a valid reason for this statement? 

a)

Reflexive property of congruence

b)

Definition of angle bisector

c)

Symmetric property of congruence

d)

Corresponding angles are congruent

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