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Millau BridgeSir Norman Foster

Point, Lines, Planes, Angles

FallingwatersFrank Lloyd Wright

Millenium ParkFrank Lloyd Wright

1.3 Segments, Rays, and DistanceWE 5

1.3 Segments, Rays, and DistanceWE Page 15

The numbers given are coordinates of 2 points on a number line. Find the distance between the points.

1. - 6 and 9 2. - 3 and - 17

3. - 1.2 and - 5.7 4. - 2.5 and 4.6

9 ( 6) 15 17 ( 3)

17 3 14

1.2 ( 5.7)

1.2 5.7 4.5 4.6 ( 2.5)

4.6 2.5 7.1

In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.

5. H

KM

T

L

LM MH

HL KT��

HL

True. It goes through midpoint.

True. The order of the letters doesn’t matter.


5.

6. KM must = MT

H

KM

T

L

LM MH

HL KT��

HL

False. KM < MT



5.

6. KM must = MT

7. bisects

8. is a bisector of

H

KM

T

L

LM MH

HL KT��

HL

MT LH

LHKT��



False. KM < MT


9. and are opposite rays.

10. and are opposite rays.

11. is the same as

12. is the same as

H

KM

T

L

MT��

TM��

False. They do not have the same endpoint.

MT��

MK��

LH��

HL

KT��

KM��

True.

False. One’s a line & the others a segment.

True. They have same starting point and direction.


HL KT��

HL

13. is the same as

14. is the same as

15. HM + ML = HL

H

KM

T

L


HL KT��

HL

KT��

KM��

KT��

KM

True. Same line but different points.


True. Segment Add. Postulate.

13. is the same as

14. is the same as

15. HM + ML = HL

16. TM + MH = TH

H

KM

T

L


HL KT��

HL

KT��

KM��

KT��

KM

True. Same line but different points.


True. Segment Add. Postulate.

False. Shortest distance between 2 points is a straight line.

17. T is between H and M.

18. M is between K and T.

H

KM

T

L


HL KT��

HL

False. T is not on segment HM.

True. M is on segment KT.

Name each of the following.

19. The point on whose distance from D is 2.

DB C GFEA

- 3 - 2 - 1 0 1 2 3

DA��

B




DB C GFEA

- 3 - 2 - 1 0 1 2 3

DA��

DG��

B

F


21. Two points whose distance from E is 2.

DB C GFEA

- 3 - 2 - 1 0 1 2 3

C and G


21. Two points whose distance from E is 2.

22. The ray opposite to

DB C GFEA

- 3 - 2 - 1 0 1 2 3

BE��

C and G

BA��


23. The midpoint of

DB C GFEA

- 3 - 2 - 1 0 1 2 3

BF

D seen visually. orAverage the coordinates.

2 20

2

Note that the name of the midpoint is a letter while the coordinate is a number.

D


24. The coordinate of the midpoint of

DB C GFEA

- 3 - 2 - 1 0 1 2 3

-1 seen visually. or

Average the coordinates.

2 01

2

BD



DB C GFEA

- 3 - 2 - 1 0 1 2 3

AE

-1



26. A segment congruent to

DB C GFEA

- 3 - 2 - 1 0 1 2 3

AE

BGAF

-1

In Exercises 27-30 draw and so that the

conditions are satisfied.

27. Segments CD and RS intersect, but neither segment bisects to other.

28. Segment CD and RS bisect each other.

R

SC

D OR R S

C

D

OR

R

S

C

D

R

S

C

D

CD RS

There are an infinite possibilities.


29. bisects but doesn’t bisect

OR

R S

C

D

R SC

D


conditions are satisfied.CD RS

CDCD

RSRS


30. and do not intersect.

ORC

R

DS

R

DC

S


conditions are satisfied.CD RS

CD RSBut and do intersect. CD��

RS�� There are an

infinite possibilities.

31. In the diagram, , S is midpoint of .

QR = 4 and ST = 5. Complete.

PR RT RT

P Q R S TLabel DiagramFirst !! 4 5 5

1010

6

a] RS = _____ b] RT = _____

c] PR = _____ d] PQ = _____

5 10

10 6Note that once the diagram was labeled, everything was easier.

32. In the diagram, X is the midpoint of

VW = 5, and VY = 20. Find the coordinates of W, X, & Y.

VZ

V W X Y Z

5

20

34- 12 22

17 17

Label Diagram

22 ( 12) 34

X = -12+17 = 5W = -12+ 5 = -7

Y = -12+20 = 8

33. DE = 5x + 3 , EF = 33

E is the midpoint of . Find the value of x.

F

D

HG E

DF

5x + 3 = 33

5x = 30

x = 6

33

5x + 3

Label the diagram first

34. DE = 45 , EF = 5x - 10


F

D

HG E

DF

45 = 5x - 10

55 = 5x

11 = x

5x - 10

DE = 45


35. DE = 3x , EF = x + 6


F

D

HG E

DF

3x = x + 6

2x = 6

X = 3

EF = x + 6

DE = 3x


36. DE = 2x - 3 , EF = 5x - 24


F

D

HG E

DF

2x – 3 = 5x - 24

-3x -3 = -24

- 3x = - 21

x = 7

Label the diagram firstCC5x - 24

2x – 3

37. GE = y , EH = y – 1 , GH = 11

Find the value of y.

F

D

HG E

y + y - 1 = 11

2y - 1 = 11

2y = 12x = 6

Segment Addition Postulate

Sum of the parts = the whole.

y y – 1Label the diagram first

GH = 11

38. GE = 3y , EH = 24 , GH = 7y - 4

Find the value of y.

F

D

HG E

3y + 24 = 7y - 4

24 = 4y - 4

28 = 4y

7 = y



3y 24Label the diagram first

GH = 7y - 4

39. GE = z + 2 , EH = 2z - 6 , GH = 20

Find the value of z. Then find GE and EH and state whether E is the midpoint.

F

D

HG E

z + 2 + 2z - 6 = 20

3z - 4 = 20

3z = 24

z = 8



GE = z + 2 = 10

EH = 2z – 6 = 10

E is a midpoint.

z + 2 2z - 6Label the diagram first

GH = 20

Not done yet. Find segments.

40. GE = z , EH = 2z - 4 , GH = z + 6

Find the value of z. Then find GE and EH and state whether E is the midpoint.

F

D

HG E

z + 2z - 4 = z + 63z - 4 = z + 6

2z - 4 = 6

2z = 10



GE = z = 5

EH = 2z – 4 = 6

E is not a midpoint.

z = 5

z 2z - 4Label the diagram first

GH = z + 6

41.

Name the graph of the given equation or inequality.

2 2x NH M ZYTG

- 4 - 2 0 2 4 6 8

42. 0x

HN

MH or MG��

43. 4x

4 4x GT

44.

Name the graph of the given equation or inequality.

0x NH M ZYTG

- 4 - 2 0 2 4 6 8

45. 0x

GH��

The whole line.

Point M

The absolute value of negative numbers are greater than 0; the absolute value of 0 = 0 ; and the absolute value of positive numbers are greater than zero.

46a.

Draw the diagram and illustrate your answer.

46b.

On , how many points are there whose distance

from point A is 3 cm.

AB��

3 cm

A

B

1

On , how many points are there whose distance

from point A is 3 cm.

AB��

3 cm 3 cm

A

2

B

C’est fini.

Good day and good luck.

ac1.3hmorepracticeproblems

Education

true of false

label diagram x

f d h g e

midpoint ofd b c g f

mt true

midpoint of26

midpoint ofvw

c r d s r d c s