Medians and Altitudes in Triangles

​6.3 Medians and Altitudes of Triangles

​

" Life itself is your teacher, and you are in a state of constant learning."

-Bruce Lee

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Multiple Choice

Which of the following words describes the point shown in the figure? #6

• A. Centerpoint

• B. Orthocenter

• C. Centroid

• D. Midpoint

Multiple Choice

The figure is an example of a(n) ...#1

• angle bisector

• midsegment

• altitude

• median

Multiple Choice

The centroid is the point of concurrency of the ________________ of a triangle. #11

• Medians

• Altitudes

• Perpendicular Bisectors

• Angle Bisectos

Multiple Choice

If Z is the centroid, what type of segments are drawn? #5

• angle bisectors

• perpendicular bisectors

• altitudes

• medians

Multiple Choice

CF, BE, and AD are the medians of the triangle. If BF =10, find AF. #2

• 20

• 10

• 5

• Not Enough Information

Multiple Choice

[Medians and Centroid]

If AC = 16, what is the length AM? #8

REMEMBER: POINT M IS THE MIDPOINT OF AC.

• 4

• 8

• 6

• 10

Multiple Choice

In ΔABC, Q is the centroid. Find QM. #12

HINT!!! USE THE CENTROID RATIO THEOREM

2(SHORTER PART OF MEDIAN) = (LONGER PART OF MEDIAN)

• 12

• 6

• 18

• 4

Multiple Choice

In ΔABC, Q is the centroid. Find CL. #13

HINT!!! USE THE CENTROID RATIO THEOREM

2(SHORTER PART OF MEDIAN) =(LONGER PART OF MEDIAN)

• 3

• 6

• 9

• 2

Multiple Choice

If BL = 12 and point P is the centroid, what is PL? #27

• 3

• 4

• 8

• 10

Fill in the Blanks

Find x if LI = 3x + 9 and IA=15 #3

HINT!!! USE THE CENTROID RATIO THEOREM

2(SHORTER PART OF MEDIAN) =(LARGER PART OF MEDIAN)

Multiple Choice

Which of the following describes a median of a triangle? #7

• 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.

Multiple Choice

In ΔABC, Q is the centroid. Find CL. #13

HINT!!! USE THE CENTROID RATIO THEOREM

2(SHORTER PART OF MEDIAN) =(LONGER PART OF MEDIAN)

• 3

• 6

• 9

• 2

Multiple Choice

BE = 15. Find EG. #10

HINT!!! USE (1/3) (WHOLE MEDAN) = (SHORTER PART OF MEDIAN)

• 10

• 5

• 22.5

• 20

Multiple Choice

Given TO=7a+5 and OR=8a, find the value of "a" and the length of TR. #18

• a=5, TR=40

• a=4, TR=70

• a=5, TR=80

• a=4, TR=81

Fill in the Blanks

What is the length of segment NS? #19

Multiple Choice

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units.

What is AF? #20

• 51

• 11

• 15

• 43

Multiple Choice

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet.

What is RS? #21

• 4 feet

• 7 feet

• 10 feet

• 14 feet

Fill in the Blanks

Find the x value of the centroid of a triangle whose vertices are (1, 10) (-7, 2), and (-3, 7). #45

Fill in the Blanks

Find the y value of the centroid of a triangle whose vertices are (1, 10) (-7, 2), and (-3, 7). Round to the nearest hundredth. #46

Multiple Choice

The three altitudes of a triangle intersect at the? #41

• Circumcenter

• Incenter

• Centroid

• Orthocenter

Multiple Choice

What type of special segments are being used? #42

• Perpendicular Bisectors

• Angle Bisectors

• Medians

• Altitudes