MEASURING

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MEASURING SEGMENTS AND ANGLES
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Assignment Page 29 - 30 2 30 even 31, 32, 34,
36, 42, 44, 46, 70, 72, 76, 78
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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
B
A
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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
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A B C D E
Compare CD and DE CD -2 0 -2
2 DE 0 2 - 2 2 CD DE
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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
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4x 20 2x 30
E F
G
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
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3x 1 2x-2
E F
G
EG 64 Find EF and FG
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AB 5x 3 and BC 7x 9 Find AC
A B
C
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Midpoint of a Segment point that divides the
segment into two congruent segments We are
bisecting the segment
A B
C AB BC
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5x 3 7x 9 P
T Q
Using midpoint
T is midpoint, find PT, TQ and PQ
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
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Angles two rays with the same endpoint rays are
the sides of the angle the endpoint is the
vertex
vertex
rays
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A
Naming angles
D
1
2
B
lt1 Use the number ltADB ltBDA Name the two sides
with the vertex in the middle If we were
referring to ltADC we could also say that this was
ltD
C
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Measuring Angles Use a Protractor Classify
Angles according to their measurement acute
less than 90 degrees 0 lt x lt 90
x
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Right angle exactly 900 x 90 Obtuse
angle greater than 900 but less than 1800 90 lt
x lt 180
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Straight angle two opposite rays 1800
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Angle Addition Postulate If point B is in the
interior of lt AOC, the mltAOB mltBOC m ltAOC
In other words, if you have two small adjacent
angle they will add up to the larger angle
B
A
C
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If lt AOC is a straight angle, the mltAOB mltBOC
180
B
O
A
C
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Try this! If mltDEG 145, find the mltGEF
G
D
E
F
145 x 180 x 35 mlt GEF 350
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Congruent Angles Angles that has the same
measure These angles can be marked to show they
are congruent