ac1.3hmorepracticeproblems

Millau BridgeSir Norman Foster

Point, Lines, Planes, Angles

FallingwatersFrank Lloyd Wright

Millenium ParkFrank Lloyd Wright

1.3 Segments, Rays, and DistanceWE Page 15

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.

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

5.

6. KM must = MT

H

KM

T

L

LM MH

HL KT�������������� �

HL

False. KM < MT

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

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

5.

6. KM must = MT

7. bisects

8. is a bisector of

H

KM

T

L

LM MH

HL KT�������������� �

HL

MT LH

LHKT�������������� �

True. It goes through midpoint.

True. It goes through midpoint.

False. KM < MT

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

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.

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

HL KT�������������� �

HL

13. is the same as

14. is the same as

15. HM + ML = HL

H

KM

T

L

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

HL KT�������������� �

HL

KT�������������� �

KM�������������� �

KT�������������� �

KM

True. Same line but different points.

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

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

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

HL KT�������������� �

HL

KT�������������� �

KM�������������� �

KT�������������� �

KM

True. Same line but different points.

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

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

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

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

Name each of the following.

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

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

DB C GFEA

- 3 - 2 - 1 0 1 2 3

DA��������������

DG��������������

B

F

Name each of the following.

21. Two points whose distance from E is 2.

DB C GFEA

- 3 - 2 - 1 0 1 2 3

C and G

Name each of the following.

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��������������

Name each of the following.

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

Name each of the following.

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

Name each of the following.

25. The coordinate of the midpoint of

DB C GFEA

- 3 - 2 - 1 0 1 2 3

AE

-1

Name each of the following.

25. The coordinate of the midpoint of

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.

There are an infinite possibilities.

29. bisects but doesn’t bisect

OR

R S

C

D

R SC

D

In Exercises 27-30 draw and so that the

conditions are satisfied.CD RS

CDCD

RSRS

There are an infinite possibilities.

30. and do not intersect.

ORC

R

DS

R

DC

S

In Exercises 27-30 draw and so that the

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

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

F

D

HG E

DF

45 = 5x - 10

55 = 5x

11 = x

5x - 10

DE = 45

Label the diagram first

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

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

F

D

HG E

DF

3x = x + 6

2x = 6

X = 3

EF = x + 6

DE = 3x

Label the diagram first

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

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

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

Segment Addition Postulate

Sum of the parts = the whole.

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

Segment Addition Postulate

Sum of the parts = the whole.

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

Segment Addition Postulate

Sum of the parts = the whole.

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.