Transcript Industrial Supremacy

GEOMETRY: CHAPTER 1
CHAPTER 1.3: Segments
and Their Measures
A postulate or axiom is a rule
that is accepted without
proof.
A theorem is a rule that can
be proved.
Postulate 1: Ruler Postulate
The points on a line can be matched one to one
with the real numbers. The real number that
corresponds to a point is the coordinate of
the point.
The distance between two points A and B ,
written as AB , is the absolute value of the
difference of the coordinates of A and B.
Postulate 2: 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.
Congruent Segments are segments that have the
same length.
In the diagram below, you can say “the length of
segment AB is equal to the length of segment
CD. You can also say “segment AB is
congruent to segment CD.” The symbol 
means “is congruent to.”
Ex. 2: Plot E (1 , 2) , F (5 , 2), G (3 ,4), and
H(3 , -1). Then determine whether segment
EF is congruent to segment GH.
To find the length of a horizontal segment,
find the absolute value of the difference of
the x-coordinates of the endpoints.
Use Ruler Postulate
EF  5  1  4
To find the length of a vertical segment, find
the absolute value of the difference of the ycoordinates of the endpoints.
Use
Ruler
Postulate
GH  4  (1)  5
Segment EF is not congruent with segment
GH.
The Distance Formula (p.19)
Recall from the Pythagorean Theorem
that, for a right triangle with
hypotenuse of length c and sides of
length a and b, you have
a2 + b2 = c2 Pythagorean Theorem
The Distance Formula (cont.)
Suppose you want to
determine the distance
d between two points
(x1,y1) and (x2,y2) in the
plane. With these two
points, a right triangle
can be formed.
The distance d between the points (x1,y1) and
(x2,y2) in the plane is
d = ( x2  x1 )2  ( y2  y1 )2
Ex. 3. Find the distance between the
points (-1,3) and (5, -2)
( x2  x1 ) 2  ( y2  y1 ) 2
(5  (1)) 2  (2  3) 2 Step 1—Use the Distance Formula
 (6) 2  (5) 2
Step 2—Simplify.
 36  25
 61
 7.81
Step 3—Use a calculator to
approximate the value of the
square root