WorksheetsMalachy & Brandon Centers of Triangles
Total questions: 20
Worksheet time: 30mins
The centroid cuts each median into two segments. The shorter segment is ___________ the length of the entire segment.
one third
two thirds
three fourths
one half
The circumcenter is equidistant from each ______________ of the triangle
vertices
sides
median
altitude
The incenter is equidistant from each __________ of the triangle.
vertices
sides
median
altitude
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.
-2.33333
-3.11116
-2.66666
Not enough info
How many angle bisectors are needed to find the incenter.
1
2
3
4
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?
160 yards
175 yards
165 yards
180 yards
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?
7.5 yards
7.25 yards
1.75 yards
1.66 yards
If the circumcenter is 6 feet from the centroid how far is the centroid to the orthocenter? Picture not to scale.
9 feet
18 feet
12 feet
6 feet
If AP = 12, what is AL?
6
12
18
24
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.
not possible
CD: 5, BD:4
CD: 4.0457, BD: 2.480
CD: 5.9234, BD: 3.6841
CD: 2.66, BD: 1.9349
Which center(s) of triangles can be located outside of the triangle?
Orthocenter
Orthocenter, Centroid
Circumcenter
Centroid
Incenter
Which Centers of triangles fall on the euler line?
Orthocenter, Circumcenter, Centroid
Centroid, Incenter, Orthocenter
Orthocenter, Centroid
Incenter, Centroid, Circumcenter
SELECT ALL OF THE CORRECT ANSWERS OR IT WILL NOT BE CORRECT
Which triangle(s) are congruent to each other.
Tri RUQ & Tri PQU
Tri TPR & Tri TPQ
Tri QSR & PSR
None of the triangles
If Triangle ABC is inscribed with Circle D point D is the _________ and Line BC is a __________ to Circle D.
Incenter, Chord
Circumcenter, Tangent
Incenter, Tangent
Circumcenter, Chord
If you find the circumcenter of an obtuse triangle where is it located?
Outside the triangle
Inside the triangle
On the longest side of the triangle
It depends on the value of the largest angle
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.
137.5 square units
138.1 square units
133.4 square units
134.2 square units
