Median and Altitude of a Triangle

Orthocenter

• the lines containing the altitudes of a triangle are concurrent, intersecting at a point called the orthocenter.

Centroid

• The point of intersection for all 3 medians

• In this figure, the centroid is at Point P

Altitude of a triangle

• a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side.

• An "Altitude" can be interior or exterior to the triangle.

• Every triangle has 3 altitudes.

Multiple Choice

Fill in the blank.
All three medians intersect at the point of concurrency called the ____________.

• Incenter
• Circumcenter
• Orthocenter
• Centroid

Multiple Choice

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

• angle bisector

• dotted line theorem

• altitude

• median

Multiple Choice

In ΔXYZ, YB, XC, and ZA are medians.

If YC= 10, then ZC = _______

• 15

• 5

• 20

• 10

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

In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.

If XP = 8, then PC = _______

• 2.7

• 12

• 5

• 4

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

Fill in the blanks.
Medians connect the __________ to the opposite ________.

• hypotenuse; leg
• leg; hypotenuse
• vertex; leg
• leg; vertex

Multiple Choice

Fill in the blank.
Altitudes hit the ground at _______ degrees.

• 180
• 90
• 60
• 360

Multiple Choice

Which of the following describes a median of a triangle?

• A. A middle of the triangle.
• 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. 

Multiple Choice

The altitude is __________to the side of a triangle.

• parallel
• skew
• off
• perpendicular

Multiple Choice

Name the segment/line/ray shown in the picture.

• Perpendicular Bisector

• Angle Bisector

• Median

• Altitude

Multiple Choice

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

• angle bisectors
• perpendicular bisectors
• altitudes
• medians

Multiple Choice

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

• 3

• 6

• 9

• 12

Multiple Choice

In $$\angle PON$$  , OP is the altitude of MN. If  is 4x - 13 and  $$\angle ONP$$  is 2x-5, find the m $$\angle PON$$  

• 90

• 18

• 59

• 69

Multiple Choice

GT is the median. If FT is 3x + 8 and TE is 7x - 16, find the value of x

• 6

• 24

• 9.8

• 48

Multiple Choice

The INCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

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

• angle bisector
• perpendicular bisector
• median
• midsegment

Multiple Choice

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

• Medians
• Midsegments
• Perpendicular Bisectors
• Angle Bisectos

Multiple Choice

The altitudes of a triangle intersect at the _________________________.

• Centriod
• Circumcenter
• Incenter
• Orthocenter

Multiple Choice

Find the value of x

• x=28
• x=14
• x=23
• x=46

Multiple Choice

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

• 20
• 10
• 5
• Not Enough Information

Multiple Select

Which types of centers are ALWAYS INSIDE the triangle? (Select all that apply)

• Orthocenter

• Incenter

• Centroid

• Circumcenter

Multiple Choice

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

• obtuse

• acute

• iscolese

• right