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Malachy & Brandon Centers of Triangles

Total questions: 20

Worksheet time: 30mins

Name
Class
Date
1.

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

2.
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
3.
If G is the centroid of triangle ABC and BE= 18. Find the length of BG.
a)
6
b)
12
c)
18
d)
Not Enough Information
4.

The circumcenter is equidistant from each ______________ of the triangle

a)

vertices

b)

sides

c)

median

d)

altitude

5.

The incenter is equidistant from each __________ of the triangle.

a)

vertices

b)

sides

c)

median

d)

altitude

6.

A new monument is being built in Maplewood. The monument needs to be at a point that is equidistant from the three main roads that intersect in a triangle. Locate this point so that any person will be able to get to the monument by the shortest route possible. Road B is 7x-3 miles from the monument. Road C is 10x+4 miles from the monument. What is x.

a)

-2.33333

b)

-3.11116

c)

-2.66666

d)

Not enough info

7.

How many angle bisectors are needed to find the incenter.

a)

1

b)

2

c)

3

d)

4

8.

G is a centroid. Eleanor is located at point A. Jack is located at point D. Jack is x+16 yards away from point G. Eleanor is 3x-12 yards away from point G. How far away from each other are they?

a)

160 yards

b)

175 yards

c)

165 yards

d)

180 yards

9.

Point A is the circumcenter of triangle BCD. Eleanor is at point B, Jack is at point C, and Brandon is at point D. Jack is 17x-12 yards from the point A. Brandon is 3x+2 yards from point A. How far from the center is Jack?

a)

7.5 yards

b)

7.25 yards

c)

1.75 yards

d)

1.66 yards

10.
If Z is the centroid, what type of segments are drawn?
a)
angle bisectors
b)
perpendicular bisectors
c)
altitudes
d)
medians
11.

If the circumcenter is 6 feet from the centroid how far is the centroid to the orthocenter? Picture not to scale.

a)

9 feet

b)

18 feet

c)

12 feet

d)

6 feet

12.

If AP = 12, what is AL?

a)

6

b)

12

c)

18

d)

24

13.
IJ is a midsegment of triangle MLN. What is the length of segment IJ?
a)
9
b)
6
c)
18
d)
0
14.

3 busy roads form a triangle. You want to buy a house equidistant from all three roads. Road AB is 15 blocks, road BC is 8 blocks, and road AC is 17 blocks. The incenter in point D. Angle A can be bisected by line AE into two 20 degree angles. Also, angle ADB is 140 degrees. Line AD is 5 blocks. How far is point B to D and C to D on this weird neighborhood.

a)

not possible

b)

CD: 5, BD:4

c)

CD: 4.0457, BD: 2.480

d)

CD: 5.9234, BD: 3.6841

e)

CD: 2.66, BD: 1.9349

15.

Which center(s) of triangles can be located outside of the triangle?

a)

Orthocenter

b)

Orthocenter, Centroid

c)

Circumcenter

d)

Centroid

e)

Incenter

16.

Which Centers of triangles fall on the euler line?

a)

Orthocenter, Circumcenter, Centroid

b)

Centroid, Incenter, Orthocenter

c)

Orthocenter, Centroid

d)

Incenter, Centroid, Circumcenter

17.

SELECT ALL OF THE CORRECT ANSWERS OR IT WILL NOT BE CORRECT


Which triangle(s) are congruent to each other.

a)

Tri RUQ & Tri PQU

b)

Tri TPR & Tri TPQ

c)

Tri QSR & PSR

d)

None of the triangles

18.

If Triangle ABC is inscribed with Circle D point D is the _________ and Line BC is a __________ to Circle D.

a)

Incenter, Chord

b)

Circumcenter, Tangent

c)

Incenter, Tangent

d)

Circumcenter, Chord

19.

If you find the circumcenter of an obtuse triangle where is it located?

a)

Outside the triangle

b)

Inside the triangle

c)

On the longest side of the triangle

d)

It depends on the value of the largest angle

20.

You bought a triangular plot of land (ABC) and want to figure out the area of different parts of it. Use the information given in the picture above to find the area of Triangle AGF. G is the centroid. Do not round before final answer. Do not assume anything and not drawn to scale.

a)

137.5 square units

b)

138.1 square units

c)

133.4 square units

d)

134.2 square units