Altitudes, Medians, Perpendicular Bisectors,

and Parallel Line TheoremReview Activity

November 17, 2011

Points

3 – First answer done completed correctly

1 – To all groups who had the correct answer but was not first one completed

Bonus Round:

Teams work together to solve the problem.Each team must wager 1, 2, 5, or 10 points.So answer correct you receive those points, if it is incorrect you loose those points

1

x

34

Find the Value of x

X = 17

—

—

=

=

2

7

2x

Find the Value of x

X = 7

—

=

—

=

3

x - 8

35

Find the Value of x

X = 25.5

=

= —

—

4

3x

4x+20

Find the Value of x

X = 10—

—

=

=

5X

A B

YC

Z

—

—

—— = =

=

=

AB is parallel to ______

BC is parallel to ______

YZ

XY

6X

BA

YC

Z

—

—= =

=

=

——

If AC = 3x+1, and XZ=10x-6

Then AC=____7

6X

BA

YC

Z

—

—= =

=

=

——

If CB=x-1, and XY=3x-7 then XY=_____If angle XYZ=48, then angle XAB=_____If angle XBA=37, then angle XZY=_____

Bonus 1

54837

7

If three ________ lines cut off ___________ segments on one ___________, then they cut off _________ segments on every __________.

parallelcongruenttransversal

congruenttransversal

8

What is a segment from the vertex of the triangle to the

midpoint of the opposite side?

Median

9

What is the definition of an Altitude?

The perpendicular segment from a vertex of the triangle to the segment that contains the opposite side.

10

A line that contains the ___________ of one side of a triangle and is _________ to

another side passes through the _________ of the third side.

midpointparallel

midpoint

11

What is a line that is perpendicular to a segment at its midpoint and does NOT have to start at a vertex?

Perpendicular Bisector

12

The segment that joins the midpoint of two sides of a triangle….1)

2)

Is parallel to the third side

Is half as long as the third side

Bonus 2

Definition of a Centroid

Altitude fact about right triangles

Altitude fact about obtuse triangles

The point where all three medians meet

Two of the altitudes of are the legs of the triangle

Two of the altitudes are outside of the triangle

13

NM

X

Y Z

If M is the midpoint of XY and MN is parallel to YZ, then line MN is the altitude.If M is the midpoint of XY and MN is parallel to YZ, then N is the midpoint of XZ

Error Section!!

14

1810

22 20

12

15

—

—Both blue lines are a good representation of altitudes.

Both blue lines are a good representation of medians NOT altitudes.

= =

16

—

—

Both lines are a good representation of Perpendicular Bisectors.

The orange line are a good representation of Perpendicular Bisectors. The green line is not able to be determined.

17 These three lines are a good representation of Medians.

The teal line is a good representation of a Median. The blue and red lines are good representations of Altitudes.

18 The intersection of AF, BE, and CD is the centroid.

No it is not the centroid. Centroids are formed from medians. Altitudes are displayed here.

Bonus 3

NM

Y

X

Z

MN is the perpendicular bisector of XY, XZ, and YZ.

If M is the midpoint of XY and N is the midpoint of XZ, then MN || YZ and MN = 1/2 YZ.

19

A

B

C

What is the red line an example of?Explain your answer.

A Median

20

What is the red line an example of?Explain your answer.

An Altitude

A

B

CD

21M

L N

What is the black line an example of? Explain your answer.

A Perpendicular Bisector

22

NM

Y

X

Z

Why are these true?If MN = 6, then YZ = 12.If YZ = 20, then MN = 10.

Just needs an explanation

23

What is the red line an example of? Explain your answer.

Altitude, Median, and Perpendicular Bisector

24

What is the yellow line an example of? Explain your answer.

None, explain

Bonus 4

A

B

C

What are each of these lines? Explain.

Red is Altitude, orange is Median, and grey is Perp. Bisector

25

R

3

K

J

S

4

What is the length of JK? You will be asked to justify your answer.

JK = 6

26

Construct a Right Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector.

Be ready to justify your answer.

27

Construct an Acute Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector.

Be ready to justify your answer.

28

Be ready to justify your answer.

Construct an Obtuse Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector.

2912

JK = 24

—

=

— =

J

KFind JK.Be ready to justify your answer.

3010x

X = 3

—

=

— =

J

KFind x.Be ready to justify your answer.

15x

+15

Bonus 5

Construct a Centroid.

Be ready to justify your answer.