Download Measuring Segments and Angles

1-3 and 1-4 Measuring
Segments and Angles
Postulate 1-5 Ruler Postulate
The point of a line can be put into a oneto-one correspondence with the real
number so that the distance between any
two points is the absolute value of the
difference of the corresponding numbers.
AB = | a – b |
B
A
4
10
Two segments with the same length are
congruent.
If AB = CD, then AB ≅ CD
≅ means congruent
B
6
A
B
A
D
6
C
D
C
Postulate 1-6 Segment Addition
Postulate
If three points A, B, and C
are collinear and B is
between A and C, then
AB + BC = AC
C
B
A
If GJ = 32,
• find x
• find GH
• find HJ
If AX = 45,
• find y
• find AQ
• find QX
A midpoint of a segment is a point
that divides the segment into two
congruent segments.
A
B
C
• B is the midpoint
of AC
• AB
M is the midpoint
of RT
• find x
• find RM
• find RT
BC
An angle  is formed by two rays (called
sides of the angle) with the same
endpoint (called the vertex of the angle).
Angles are measured in degrees.
Sides are GC and GA; G is the vertex.
Name this angle:
G
3
CGA
AGC
Postulate 1-7 Protractor Postulate
Let OA and OB be opposite rays in a plane. OA, OB
and all the rays with endpoint O that can be drawn on one
side of AB can be paired with the real number from 0 to 180
in such a way that:
a. OA is paired with 0 and OB is paired with 180
b. If OC is paired with x and OD is paired with y,
then mCOD = | x – y |
D
C
B
O
A
Angles can be...
x
°
Acute: 0 < x < 90
x
°
Obtuse: 90 < x < 180
x
°
Right: x = 90
x
°
Straight: x = 180
Postulate 1-8 Angle Addition Postulate
If point B is in the interior of AOC, then
mAOB + mBOC = m AOC.
•
•
If AOC is a straight angle, then
mAOB + mBOC = 180.
Angles with the same measure are
congruent.
If m1 = m2, then 1  2
Congruent
“curtains”