Centers of Triangles Test Review

Centers of Triangles Test Review

​Perpendicular Bisector Theorem

Multiple Choice

Given you have two points and are asked to find the perpendicular bisector, what step should you do first?

• Skip the problem
• Find the distance between the two points
• Find the equation of the line
• Find the midpoint of the two given points

Multiple Choice

If you found the midpoint of line segment AB, what should you do next to find the equation of the perpendicular bisector?

• Use the midpoint and one of the points from AB to write the equation
• Use the midpoint and slope perpendicular to AB to write the equation
• Use the distance and midpoint to find the equation
• Skip it and hope it's not a test question

Multiple Choice

Write the equation of the perpendicular bisector of the line AB given:
A(3,-3) & B(1,-1)

• y = x - 4
• y = x + 4
• y = 1/2x -4
• y = x + 2

Multiple Choice

Write the equation of the perpendicular bisector of the line AB given:
A(1,3) & B(-3,5)

• y = 2x + 4
• y = 2x + 6
• y = -2x + 6
• y = 2x - 6

Multiple Choice

Write the equation of the perpendicular bisector of the line AB given:
A(3,1) & B(-3,6)

• y = -5/6x + 7/2
• y = 6/5x + 9/2
• y = 6/5x + 7/2
• y = 6/5x + 4

​Partitioning a Line Segment

Multiple Choice

6) The ratio is 3:1. How many parts are there?

• 2

• 3

• 4

• 5

Multiple Choice

Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3.

The coordinates of the point P are:

• (1,5)

• (0,4)

• (3, 1)

• (-1, 1)

Multiple Choice

Given the points A(-2 4) and B(7, -2), find the coordinates of the point P on directed line segment AB in the ratio 1:2.

The coordinates for point P are:

• (0, 1)

• (0, -1)

• (1,2)

• (2,1)

Multiple Choice

Find the coordinates of P so that P partitions segment AB in the ratio 5:1 with A(2, 4) and B(8, 10).

• (7,9)

• (9,7)

• (-3,9)

• (5,1)

​Midsegment Theorem

Multiple Choice

What segment is parallel to EF?

• Segment PM
• Segment MN
• Segment NP
• Segment FG

Multiple Choice

QR is a midsegment of triangle WUV. What is the length of segment QR?

• 4
• 8
• 16
• 32

Multiple Choice

What is the measure of angle X?

• 60
• 40
• 140
• 100

Multiple Choice

What is the measure of angle Y?

• 60
• 40
• 140
• 100

Multiple Choice

QR is a midsegment of triangle WXY. What is the length of segment WY?

• 3
• 6
• 9
• 12

Multiple Choice

QR is a midsegment of triangle FGH. Solve for the value of x?

• 5.5
• 11
• -5.5
• -11

Multiple Choice

QR is a midsegment of triangle BCD. Solve for the value of x.

• 11
• 18
• 9
• -7

Multiple Choice

UV is a midsegment of triangle FGH. What is the length of segment UV?

• 12
• 10
• 5
• -12

​Centroid which is created by medians

Multiple Choice

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

• Medians
• Midsegments
• Perpendicular Bisectors
• Angle Bisectos

Multiple Choice

If Z is the centroid, what type of segments are drawn?

• angle bisectors
• perpendicular bisectors
• altitudes
• medians

Multiple Choice

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

• 20
• 10
• 5
• Not Enough Information

Multiple Choice

If DL = 24, then DG = 

• 16
• 8
• 12
• 36

Multiple Choice

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

• 4
• 8
• 12
• Not Enough Information

Multiple Choice

X is the centroid of the triangle. If AZ = 24, find AX.

• 4

• 8

• 12

• 16

Multiple Choice

X is the centroid of the triangle. If ZX = 3, find AZ.

• 3

• 6

• 9

• 12

Multiple Choice

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

Multiple Choice

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

• angle bisector
• midsegment
• altitude
• median

Multiple Choice

If G is the centroid of triangle ABC and BE= 18. Find the length of BG.

• 6
• 12
• 18
• Not Enough Information

Multiple Choice

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

• 8
• 16
• 24
• Not Enough Information

Multiple Choice

If G is the centroid of triangle ABC and GE= 7. Find the length of BE.

• 7
• 14
• 21
• Not Enough Informaion

​Circumcenter - created by perpendicular bisectors

Equal distant to the

vertices of the triangle​

Multiple Choice

Define: CIRCUMCENTER OF A TRAINGLE

• the intersection point of the three perpendicular bisectors of a triangle 
• when a circle passes through the three vertices of a triangle 
• the point of intersection of three or more lines 
• the intersection point of the three angle bisectors of a triangle 

Multiple Choice

Which point is equidistant from the vertices?

• Circumcenter
• Incenter
• Neither
• Bilateral

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

Point P is the circumcenter, which segment is equal to PB

• DA
• AC
• PC
• PF

Multiple Choice

D is the circumcenter, find ED

• 15
• 16
• 17
• 19

Multiple Choice

M is the circumcenter of triangle GHI. Find GM.

Hint: you will have to use pythagorean theorem

• 30.92

• 32.41

• 34.01

• 35.74

Multiple Choice

D is the circumcenter, find EH

• 15
• 16
• 17
• 19

Multiple Choice

D is the circumcenter, find DG

• 15
• 16
• 17
• 19

Multiple Choice

H is the circumcenter of triangle BCD. Find EH.
Hint: you will have to use pythagorean theorem

• 9.45

• 10.95

• 11.25

• 12.15

​Incenter - created by angle bisectors

Equal distance to the sides

of the triangle​

Multiple Choice

Define: INCENTER OF A TRIANGLE

• the intersection point of the three angle bisectors of a triangle 
• when three or more lines intersect at a single point 
• the intersection point of the three perpendicular bisectors of a triangle 
• the point of intersection of three or more lines 

Multiple Choice

Which point is equidistant from the sides?

• Circumcenter
• Incenter
• Neither
• Bilateral

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Fill in the Blanks

G is the incenter. What is the length of BG?

Fill in the Blanks

P is the incenter of triangle JKL. Find OP.

Fill in the Blanks

P is the incenter of triangle JKL. Find ML.

Hint: you will have to use pythagorean theorem

Multiple Select

P is the incenter. Which segment lengths are equal?

• KP

• MP

• PN

• PJ

• PL

Fill in the Blanks

P is the incenter. What is the length of JP? (hint: you need to use the Pythagorean Theorem)

Fill in the Blanks

P is the incenter of triangle JKL. Find NP.

​Orthocenter - created by altitudes

​

Multiple Choice

The three altitudes of a triangle intersect at the?

• Circumcenter

• Incenter

• Centroid

• Orthocenter

Multiple Choice

What is the point of concurrency?

• Orthocenter

• Centroid

• Circumcenter

• Incenter

Multiple Choice

True or False:

An altitude goes from a vertex of the triangle to the opposite side of the triangle, creating a perpendicular angle.

• True

• False

Multiple Choice

If D is the orthocenter, which type of line segments are drawn?

• Medians

• Altitudes

• Angle Bisectors

• Perpendicular Bisectors

Mixed review - vocabulary practice

Multiple Choice

The circumcenter is the point at which all the _____ of a triangle meet.

• medians

• altitudes

• perpendicular bisectors

• angle bisectors

Multiple Choice

The incenter is the point at which all the ____ of a triangle meet.

• perpendicular bisectors

• medians

• altitudes

• angle bisectors

Multiple Choice

The centroid is the point at which the ____ of a triangle meet.

• perpendicular bisectors

• angle bisectors

• medians

• altitudes

Multiple Choice

The orthocenter is the point at which the ____ of a triangle meet.

• perpendicular bisectors

• angle bisectors

• medians

• altitudes

Multiple Choice

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

Multiple Choice

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

• angle bisector
• perpendicular bisector
• median
• midsegment

Multiple Choice

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

• angle bisector
• midsegment
• altitude
• median

Multiple Choice

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

• altitude 
• perpendicular bisector
• midsegment
• angle bisector

Multiple Choice

When you draw the medians of a triangle it creates the point of concurrency called the _____________.

• Centroid
• Incenter
• Perpendicular Bisectors
• Altitude

Multiple Choice

The altitudes of a triangle intersect at the _________________________.

• Centriod
• Circumcenter
• Incenter
• Orthocenter

Multiple Choice

The figures above are examples of ...

• altitudes

• perpendicular bisectors

• medians

• angle bisectors

Multiple Choice

The place where all three angle bisectors meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

The place where all three perpendicular bisectors meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

The place where all three medians meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

The place where all three altitudes meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

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

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

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

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

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

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

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

• Circumcenter

• Orthocenter

• Incenter

• Centroid