TOPIC 1-5: SEGMENTS, RAYS, AND DISTANCE



TOPIC 2-3: SEGMENTS AND DISTANCE

|Term |Definition |Sketch |

| | | |

|Line Segment |Part of a line consisting of two endpoints and all the points | |

| |between them. | |

| | | |

| | | |

| |Name of a Segment: | |

|Notation | | |

| |Length of a Segment: | |

To measure the LENGTH of a segment, you can use a number line to count the DISTANCE between the two endpoints.

EXAMPLE 1 Find the distance between –2 and 6 on a number

line.

EXAMPLE 2 Find PQ, QR and PR on the number line shown

below.

PQ = ____________ QR = ____________ PR = ____________

When a segment is drawn on a coordinate plane, you can find its LENGTH by using the DISTANCE formula:

EXAMPLE 3 Find the distance between ( 2, -1 ) and ( -2, -3 ).

EXAMPLE 4 Find AB.

Examine the measures of PQ, QR and PR in EXAMPLE 2. Notice that 1.5 + 4.5 = 6, so __________________. This suggests the following postulate…

Segment Addition Postulate: If Q is between P and R, then

PQ + QR = PR. If PQ + QR = PR, then Q is between P and R.

Part + Part = Whole

EXAMPLE 5 If B is between A and C and AB = 4 and BC = 5, then

AC = _______________

EXAMPLE 6 If AB = x, BC = x + 6 and AC = 24, then find AB and

BC.

AB = _______________; BC = ________________

EXAMPLE 7 Find LM if L is between N and M, NL = 6x – 5,

LM = 2x + 3 and NM = 3x + 13.

LM = _______________

NAME_________________DATE__________________PER.______

SEGMENTS AND DISTANCE

Refer to the number line below to find each measure.

| | |

|AE = _______________ |2. EC = _______________ |

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|3. EG = _______________ |4. CA = _______________ |

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Find the distance between the two given points in simplest form.

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|5. H( -3, 6 ) & C( -3, -3) |

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|HC = _______________ |

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|6. E( 9, -2 ) & G(10, -1 ) |

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|EG = _______________ |

Refer to the coordinate plane at the right to find each measure in simplest form.

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|7. FJ = ____________ |

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Given that R is between S and T, find each missing measure.

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|8. RS = 6, TR = 4.5, TS = _______________ |9. SR = 3, RT = 1, ST = _______________ |

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|10. ST = 15, SR = 6, RT = _______________ |11. TS = 11.75, TR = 3.4, RS = __________ |

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If U is between T and B, find the value of “x” and the measure of TU.

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|12. TU = 2x, UB = 3x + 1, TB = 21 |

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|x = ____________ |

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|TU = ____________ |

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|13. TU = 4x – 1, UB = 2x – 1, TB = 5x |

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|x = ____________ |

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|TU = ____________ |

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|14. TU = 1 – x, UB = 4x + 17, TB = -3x |

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|x = ____________ |

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|TU = ____________ |

REVIEW (Tell whether each statement is TRUE or FALSE. If FALSE, explain why.)

-----------------------

0

1

2

3

4

-1

-2

-3

-4

P

Q

R

d =

[pic]

A

B

A#2-3

0

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

A

B

C

D

E

F

G

[pic]

A

B

C

D

E

F

G

H

J

A#2-3 PG. 2

| | |

|_______ |15. E, B, and F are collinear. |

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|_______ |16. A, B, & C are NON-COPLANAR |

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|_______ |17. BF & BE are opposite rays. |

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|_______ |18. F and B are NON-COLLINEAR. |

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|_______ |19. There is plane through F, B, & E. |

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|_______ |The intersection of Plane M and FE is B. |

E

B

F

A

D

M

C

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