6–1 NAME DATE PERIOD DATE PERIOD 6–1 Study Guide Skills Practice

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NAME

DATE

PERIOD

6¨C1

Study Guide

NAME

DATE

Skills Practice

Medians

Medians

A median is a segment that joins a vertex of a triangle and the

midpoint of the side opposite that vertex. The medians of a triangle

intersect at a common point called the centroid. An important

theorem about medians and centroids is as follows.

AD

w

w, w

BE

w, and C

wF

w are medians of ACE.

1. If AE 24, find AF. 12

2. Find AE, if FE

The length of the segment from the vertex to the centroid is twice

the length of the segment from the centroid to the midpoint.

D

wF

w is a median of DEC.

18

36?

4. Find CE, if DE

C

M

68?

6. If AF

6

E

34

wR

T

w, Z

wX

w, and S

wW

w are medians of TXS.

In nABC, A

wN

w, B

wP

w, and C

wM

w are medians.

10, find BE.

2. If EM

3, find EC. 6

18, find TW.

9

8. If TO

26, find OR.

13

9. If WO

5, find OS. 10

T

R

S

10. Find ZO if OX

3. If EN

12, find AN. 36

4. If CM

3x " 6 and CE

50. 25

1

11. What is TZ if TS is 2?

12. What is OS if OW is 9?

Geometry: Concepts and Applications

5. If EN

x ¨C 5 and AE

X

O

Z

(Lesson 6-1)

A2

1. If BP

7. If TX

W

6!23!

18

x " 12, what is x? 8

RN

w

w, w

PM

w, and L

wO

w are medians of LNP.

13. What is LP if RL is 4? 8

x " 17, find AN. 66

14. Find AO if LO

18

6

15. What is RA if AN is 42?

Draw and label a figure to illustrate each situation.

P

21

A

M

O

R

6. NRW is a right triangle with right angle at N.

w

NX

w is a median of NRW.

N

16. If MA

13, find MP.

X

17. Find AN if RN

N

7. O

wQ

w is a median of POM.

L

R

6-7. Sample answers are given.

W

18. If LO

30.

39

20

15, find AO. 5

O

P

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Q

M

Geometry: Concepts and Applications

? Glencoe/McGraw-Hill

224

Answers

5. What is CD if CE

D

F

14

7.

3, find AE.

B

A

30

15.

3. What is BC if AC

Example:

PERIOD

Geometry: Concepts and Applications

? Glencoe/McGraw-Hill

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NAME

DATE

PERIOD

Practice

In DEF, D

wG

w, E

wH

w, and F

wIw are medians.

1. Find FG if GE

8. 8

2. Find DH if DF

10.

median a segment that joins a vertex of the triangle and the

midpoint of the side opposite that vertex

centroid the common point of intersection of the three medians

of a triangle

concurrent when three or more lines or segments meet at a

common point

5

Reading the Lesson

14

7, find DE.

1. Underline the correct word or phrase to complete each sentence.

a. Three or more lines that intersect at a common point are called

_______ lines.

(parallel/perpendicular/concurrent)

b. A triangle has (one, two, three)

___ medians.

c. The point of concurrency of the medians of a triangle is called the

_____

(vertex/centroid/center).

d. The length of the segment from the vertex to the centroid of a triangle is (onehalf/equal to/twice)

___ the length of the segment from the centroid to the midpoint.

13

2. You are given a triangle drawn on a sheet of paper with vertices labeled S, U, and

W. Write several sentences describing how to draw the median from S to U

wW

w.

50

25?

Find the midpoint of U

wW

w by constructing the bisector of the segment.

Label the midpoint M. Use a straightedge to draw S

wM

w. S

wM

w is the

median of the triangle.

41, what is XO? 20.5

3. In EGH, E

wM

w is a median. If HM

method you use to find the value.

E

In PQR, P

wS

w, w

QT

w, and R

wU

w are medians.

Geometry: Concepts and Applications

7. What is YU if RU

8. Find QY if QT

10. If PU

19.5?

24.

H

6.5

16

2x " 5, find HG. Explain the

Since E

wM

w is a median, M is the midpoint

of H

wG

w. Use the given values for HM and MG to first

solve for x. HM 5 MG (Definition of Median);

3x 2 8 5 2x 1 5 (Substitution); 3x 2 8 1 8 5 2x 1 5

G 1 8 (Add 8 to each side.); 3x 5 2x 1 13 (Simplify.);

3x 2 2x 5 2x ¨C 2x 1 13 (Subtract 2x from each

side.); x 5 13. Now, to find HG, find HM and

multiply by 2. HM 5 3(13) 2 8 5 31, so HG 5 62.

4. Meredith drew the medians of a triangle. The three medians did not meet at a single

point. Give several reasons why this may have happened. Sample answer:

Meredith may have constructed one or all of the medians incorrectly

by not finding the midpoint of the opposite side. She may also have

not been very careful in finding the midpoint, so the medians were

not exact.

Helping You Remember

14.8, what is the measure of w

YS

w? 7.4

x " 3 and UQ

M

3x ¨C 8 and MG

5. A good way to remember a new mathematical concept is to describe it in your own words.

Suppose you are given NAB with all three medians drawn and centroid at C. Median

wX

w is divided into two segments, N

wC

w and C

wX

w. Write several sentences describing the

N

relationship between the lengths of the two segments N

wC

w and C

wX

w. The length of the

2x # 17, what is x? 20

segment from the vertex to the centroid, NC, is twice the length of

the segment from the centroid to the midpoint, CX.

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Geometry: Concepts and Applications

? Glencoe/McGraw-Hill

226

Geometry: Concepts and Applications

(Lesson 6-1)

A3

5. What is JX if XM

26.

Answers

w if KX

4. Find the measure of w

XN

9. If PY

PERIOD

Key Terms

In JKL, J

wM

w, K

wN

w, and L

wO

w are medians.

6. If LX

DATE

Reading to Learn Mathematics

Medians

Medians

3. If DI

NAME

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