1-3 and 1-4 Measuring Segments and Angles

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1-3 and 1-4 Measuring Segments and Angles
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Postulate 1-5 Ruler Postulate The point of a
line can be put into a one-to-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
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Two segments with the same length are
congruent.If AB CD, then AB ? CD ? means
congruent
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Postulate 1-6 Segment Addition PostulateIf
three points A, B, and C are collinear and B is
between A and C, thenAB BC AC
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• If GJ 32,
• find x
• find GH
• find HJ

• If AX 45,
• find y
• find AQ
• find QX

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A midpoint of a segment is a point that divides
the segment into two congruent segments.

• B is the midpoint of AC
• AB ? BC

• M is the midpoint of RT
• find x
• find RM
• find RT

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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
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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
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Angles can be...
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• 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.

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Angles with the same measure are congruent. If
m?1 m?2, then ?1 ? ?2
Congruent curtains
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