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MEASURING SEGMENTS AND ANGLES. Assignment Page 29 - 30 2 – 30 even 31, 32, 34, 36, 42, 44, 46, 70, 72, 76, 78. Ruler Postulate 1- 5 The distance between any two points is the absolute value of the difference of the corresponding numbers Example: Length of AB is - PowerPoint PPT Presentation
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MEASURING
SEGMENTS
AND
ANGLES
Assignment
Page 29 - 30
2 – 30 even31, 32, 34, 36, 42, 44, 46,70, 72, 76, 78
AB
Ruler Postulate 1- 5
The distance between any two points is the absolute value of the difference of the corresponding numbers
Example:
Length of AB is
a – b which in this
Case would be 2 – 5
Or the - 3 which is 3
Congruent segments
segments of the same length
A B C D
AB = CD or AB = CD
The two tick marks is a way of showing that the two segments are congruent
A B C D E
Compare CD and DE
CD = -2 – 0 = -2 = 2
DE = 0 – 2 = - 2 = 2
CD = DE
Segment Addition Postulate 1- 6
If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC
Example :
From previous CD = 2 and DE = 2 2 + 2 = 4
CE = -2 -2 = -4 = 4 A B C D E
E F G
4x – 20 2x + 30
EG = 100. Find the value of x, then EF and FG
EF + FG = EG
(4x – 20 ) + ( 2x + 30 ) = 100
6x + 10 = 100
6x = 90
x = 15
EF = 4x – 20 = 4(15) – 20 = 40
FG = 2x + 30 = 2(15)+ 30 = 60
E F G
3x +1 2x-2
EG = 64 Find EF and FG
AB = 5x + 3 and BC = 7x – 9 Find AC
A B C
Midpoint of a Segment
point that divides the segment into two
congruent segments
We are bisecting the segment
A B C
AB = BC
Using midpoint 5x + 3 7x – 9
P T Q
PT = TQ definition of midpoint
5x + 3 = 7x – 9 substitution
5x + 12 = 7x add 9 to each side
12 = 2x subtract 5x from each side
6 = x divide each side by 2
PT = 5x + 3 = 5(6) + 3 = 33
TQ = 7x – 9 = 7(6) – 9 = 33
PQ = 66
T is midpoint, find PT, TQ and PQ
Angles
two rays with the same endpoint
rays are the sides of the angle
the endpoint is the vertex
vertex rays
Naming angles A
B
C
D 1
2
<1
Use the number
<ADB
<BDA
Name the two sides with the vertex in the middle
If we were referring to <ADC we could also say that this was <D
Measuring Angles
Use a Protractor
Classify Angles
according to their measurement
acute
less than 90 degrees
0 < x < 90x
Right angle
exactly 900
x = 90
Obtuse angle
greater than 900
but less than 1800
90 < x < 180
Straight angle
two opposite rays
1800
Angle Addition Postulate
If point B is in the interior of < AOC, the m<AOB + m<BOC = m <AOC
A B
C0
If < AOC is a straight angle, the m<AOB + m<BOC = 180
In other words, if you have two small adjacent angle they will add up to the larger angle
A
B
O C
Try this!
If m<DEG = 145, find the m<GEF
D
E
G
F
145 + x = 180
x = 35
m< GEF = 350
Congruent Angles
Angles that has the same measure
These angles can be marked to show they are congruent