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 = _______________ |
| | |
| | |
Find the distance between the two given points in simplest form.
| |
|5. H( -3, 6 ) & C( -3, -3) |
| |
| |
| |
| |
| |
| |
|HC = _______________ |
| |
|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.
| |
|7. FJ = ____________ |
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Given that R is between S and T, find each missing measure.
| | |
|8. RS = 6, TR = 4.5, TS = _______________ |9. SR = 3, RT = 1, ST = _______________ |
| | |
| | |
| | |
|10. ST = 15, SR = 6, RT = _______________ |11. TS = 11.75, TR = 3.4, RS = __________ |
| | |
| | |
If U is between T and B, find the value of “x” and the measure of TU.
| |
|12. TU = 2x, UB = 3x + 1, TB = 21 |
| |
|x = ____________ |
| |
|TU = ____________ |
| |
|13. TU = 4x – 1, UB = 2x – 1, TB = 5x |
| |
|x = ____________ |
| |
|TU = ____________ |
| |
|14. TU = 1 – x, UB = 4x + 17, TB = -3x |
| |
|x = ____________ |
| |
|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. |
| | |
|_______ |16. A, B, & C are NON-COPLANAR |
| | |
|_______ |17. BF & BE are opposite rays. |
| | |
|_______ |18. F and B are NON-COLLINEAR. |
| | |
|_______ |19. There is plane through F, B, & E. |
| | |
|_______ |The intersection of Plane M and FE is B. |
E
B
F
A
D
M
C
................
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