Geometry Section 1-2

SECTION 1-2
Line Segments and Distance

ESSENTIAL QUESTIONS
How do you calculate with measures?
How do yo ﬁnd the distance between two points?

VOCABULARY
1. Line Segment:
2. Betweenness of Points:
3. Between:

VOCABULARY
1. Line Segment: A portion of a line that is
distinguished due to having endpoints
3. Between:

VOCABULARY
AB is “segment AB”;
3. Between:

VOCABULARY
AB is “segment AB”; AB is “the measure of AB”
3. Between:

VOCABULARY
2. Betweenness of Points: For any two points A and B,
the point C will be between A and B when C is
between A and B on the line
3. Between:

VOCABULARY
2. Betweenness of Points: For any two points A and B,
the point C will be between A and B when C is
between A and B on the line
3. Between: Point K is between points J and L if and
only if (IFF) J, K, and L are collinear and JK + KL = JL

VOCABULARY
4. Congruent:
5. Rigid Transformation:
6. Congruent Segments:

VOCABULARY
4. Congruent: Two ﬁgures that have the same shape
and size
5. Rigid Transformation:

VOCABULARY
and size
5. Rigid Transformation: When a ﬁgure changes
position but keeps the same size and shape

VOCABULARY
and size
6. Congruent Segments: Any segments that have the
same measure

VOCABULARY
and size
6. Congruent Segments: Any segments that have the
same measure
AB ≅ CD is “segment AB is congruent to
segment CD”

VOCABULARY
7. Construction:
8. Distance:
9. Irrational Number:

VOCABULARY
7. Construction: The process of drawing geometric
ﬁgures using only a compass and straight edge
(ruler)
8. Distance:

VOCABULARY
(ruler)
8. Distance: The length of the segment formed
between two points

VOCABULARY
(ruler)
8. Distance: The length of the segment formed
between two points
9. Irrational Number: A number that cannot by
written as a ratio of two numbers(cannot be
written as a fraction); will be a non-repeating, non-
ending decimal

EXAMPLE 1
Use a ruler to measure the length of AC in both
metric and customary.
A C
ruler via iruler.net

EXAMPLE 1
Use a ruler to measure the length of AC in both
metric and customary.
A C
What are the values from the note sheet

EXAMPLE 2
Use a ruler to draw the following line segments.
a. YO, 2 inches long
b. QI, 12 cm long

EXAMPLE 2
Y O
b. QI, 12 cm long

EXAMPLE 2
Y O
b. QI, 12 cm long
Measure a neighbor’s drawing

EXAMPLE 3
Find HA.Assume that the ﬁgure is not drawn to scale.
7 cm 3 cm
H Y A

EXAMPLE 3
7 cm 3 cm
H Y A
HA = 7 cm + 3 cm

EXAMPLE 3
7 cm 3 cm
H Y A
HA = 7 cm + 3 cm
HA = 10 cm

EXAMPLE 4
Find RO.Assume that the ﬁgure is not drawn to scale.
17.6 in
4.3 in
R O K

EXAMPLE 4
17.6 in
4.3 in
R O K
RO = RK − OK

EXAMPLE 4
17.6 in
4.3 in
R O K
RO = 17.6 in − 4.3 in
RO = RK − OK

EXAMPLE 4
17.6 in
4.3 in
R O K
RO = 17.6 in − 4.3 in
RO = RK − OK
RO = 13.3 in

EXAMPLE 5
Find the value of x and HM if M is between H and R,
HM = 7x + 2, MR = 3x, and HR = 32 units.
H RM7x + 2 3x
32

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32
10x = 30

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32
10x = 30
x = 3

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32
10x = 30
x = 3
HM = 7x + 2

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32
10x = 30
x = 3
HM = 7x + 2
HM = 7(3) + 2

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32
10x = 30
x = 3
HM = 7x + 2
HM = 7(3) + 2
HM = 21 + 2

EXAMPLE 5
H RM7x + 2 3x
32
7x + 2 + 3x = 32
10x + 2 = 32
10x = 30
x = 3
HM = 7x + 2
HM = 7(3) + 2
HM = 21 + 2
HM = 23

DISTANCE FORMULA
d = (x2
− x1
)2
+ (y2
− y1
)2

DISTANCE FORMULA
d = (x2
− x1
)2
+ (y2
− y1
)2
for points
(x1
,y1
) and (x2
,y2
)

EXAMPLE 6
Use the number line to ﬁnd DJ.
D J
-4 -3 -2 -1 0 1 2 3 4

EXAMPLE 6
D J
-4 -3 -2 -1 0 1 2 3 4
x2
− x1

EXAMPLE 6
D J
-4 -3 -2 -1 0 1 2 3 4
x2
− x1
4 − (−4)

EXAMPLE 6
D J
-4 -3 -2 -1 0 1 2 3 4
x2
− x1
4 − (−4) 4 + 4

EXAMPLE 6
D J
-4 -3 -2 -1 0 1 2 3 4
x2
− x1
4 − (−4) 4 + 4 8

EXAMPLE 6
D J
-4 -3 -2 -1 0 1 2 3 4
x2
− x1
4 − (−4) 4 + 4 8
8

EXAMPLE 6
D J
-4 -3 -2 -1 0 1 2 3 4
x2
− x1
4 − (−4) 4 + 4 8
8 units

EXAMPLE 7
Graph A(3, 2) and B(6, 8).Then use the Pythagorean
Theorem to ﬁnd AB.

EXAMPLE 7
x
y

EXAMPLE 7
x
y
A

EXAMPLE 7
x
y
A
B

EXAMPLE 7
x
y
A
B
3

EXAMPLE 7
x
y
A
B
3
6

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2
9 + 36 = c2

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2
9 + 36 = c2
45 = c2

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2
9 + 36 = c2
45 = c2
45 = c2

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2
9 + 36 = c2
45 = c2
45 = c2
c ≈ 6.708203933

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2
9 + 36 = c2
45 = c2
45 = c2
c ≈ 6.708203933
c ≈ 6.71

EXAMPLE 7
x
y
A
B
3
6
a2
+ b2
= c2
32
+ 62
= c2
9 + 36 = c2
45 = c2
45 = c2
c ≈ 6.708203933
c ≈ 6.71units

EXAMPLE 8
Use the distance formula to ﬁnd the distance
between A(3, 2) and B(6, 8).
d = (x2
− x1
)2
+ (y2
− y1
)2

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2
d = (6)2
+ (3)2

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2
d = (6)2
+ (3)2
d = 36 + 9

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2
d = (6)2
+ (3)2
d = 36 + 9
d = 45

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2
d = (6)2
+ (3)2
d = 36 + 9
d = 45
d ≈ 6.708203933

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2
d = (6)2
+ (3)2
d = 36 + 9
d = 45
d ≈ 6.708203933
d ≈ 6.71

EXAMPLE 8
d = (x2
− x1
)2
+ (y2
− y1
)2
d = (8 − 2)2
+ (6 − 3)2
d = (6)2
+ (3)2
d = 36 + 9
d = 45
d ≈ 6.708203933
d ≈ 6.71 units

Geometry Section 1-2

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