Download 1.2 Using Segments and Congruence

1.2 Using Segments and
Congruence
Types of rules used in Geometry:
Definitions
Property/Postulate/axiom: Rule accepted without proof.
Theorem:
Rule that must be proven to be used.
Ruler Postulate
The points on a line can be assigned real number
coordinates. (think of numbers on a number line.) ! The distance between any two points is their difference.
!
(Subtract to find out how far apart they are.)
!
!
Your book reminds you to take the absolute value because you want the
distance, which must be a positive value.
EXAMPLE 1
Apply the Ruler Postulate
Measure the length of ST to the nearest tenth of a centimeter.
SOLUTION
Align one mark of a metric ruler with S. Then estimate the coordinate of T.
For example, if you align S with 2, T appears to align with 5.4.
ST = 5.4 – 2 =
ANSWER
The length of ST is about 3.4 centimeters. or ST = 3.4 cm.
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
If AB + BC = AC, then B is between A and C.
(Not all rules work both directions.)
2 segment pieces add to equal the whole segment.
Any time a segment is named
without its symbol, we are
referring to the number measurement, or length of the
segment.
Map
The cities shown on the map lie approximately
in a straight line. Use the given distances to
find the distance from Lubbock, Texas, to St.
Louis, Missouri.
SOLUTION
Because Tulsa, Oklahoma, lies between Lubbock and St. Louis, you can apply
the Segment Addition Postulate.
LS = LT + TS = 380 + 360 = 740
ANSWER
The distance from Lubbock to St. Louis is about 740 miles.
Congruent: Same size and shape.
Congruent segments have the same length.
Use the diagram to find GH.
SOLUTION
Use the Segment Addition Postulate to write an equation. Then solve the equation
to find GH.
FH
=
FG + GH
Segment Addition Postulate.
36
=
21 + GH
Substitute 36 for FH and 21 for FG.
15
=
GH
Subtract 21 from each side.
Plot J(– 3, 4), K(2, 4), L(1, 3), and M(1, – 2) in a coordinate
plane. Then determine whether JK and LM are congruent.
SOLUTION
To find the length of a horizontal segment,
find the absolute value of the difference of
the x-coordinates of the endpoints.
JK = 2 – (– 3)
Use Ruler Postulate.
To find the length of a vertical segment, find
the absolute value of the difference of the ycoordinates of the endpoints.
LM = – 2 – 3 =
ANSWER
JK and LM have the same length. So, JK ~
= LM.
Geometry
Page 12 ( 1-10, 12, 16-20ev, 21-29 odd,
32, 33, 40-45)
Sophomore Math
Day one
! Page 12 ( 1-12, 21-23, 32, 43-45)
!
Day two
! Page 12 (13-19, 24-26, 33, 40-42)
!