Download Section 1-3: Segments and Their Measures

Section 1.3:
Segments and Their Measures
Goals
Use segment postulates
Use the Distance Formula to measure distances
Anchors
•Analyze characteristics and properties of two dimensional
geometric shapes and demonstrate understanding of
geometric relationship
•Find the measure of the side of a right triangle using the
Pythagorean Theorem
1
• Postulates
Ruler Postulate
The points on any line can be matched one to
one with the real numbers. The real number that
corresponds to a pt is the coordinate of the point.
Names of
pts
A
B
x1
x2
Coordinates
of pts
2
The distance between points A and B on a number
line, written as AB, is the absolute value of the
difference between the coordinates of A and B.
AB is also called the length of AB
A
B
x1
x2
Find the distance between each of the following pairs of points:
12
37
-15
28
3
Segment Addition Postulate
• If B is between A and C,
AC
A
B
AB
C
BC
4
Given: R is between A and T. AR = 4x + 2 , RT = 3x , and
AT = 8x – 1. Find the length of each segment.
A
R
T
•Write a segment addition statement
•Substitute algebraic expressions
•Solve
•Check your answer
5
Given: O is between M and P. MO = x2 - 3 , OP = 4x - 1 ,
and MP = 8x + 1. Find the length of each segment.
M
O
P
•Write a segment addition statement
•Substitute algebraic expressions
•Solve
•Check your answer
6
Using the Distance Formula
• Distance Formula
• Congruent Segments
7
The Distance Formula
• If A(x1, y1) and B(x2, y2) are pts in a
coordinate plane, then the distance
between A and B is
8
Find the distance between the following pairs of points:
1) A ( 2 , 3 ) B ( 8 , 11 )
2) C ( 12 , 18 ) D ( 14 , 24 )
No Decimals
9
AB = 10. If A is located at ( 2 ,11) and B is
located at ( 8 , y ), what are the possible
values of y ?
AB  ( x2  x1 )  ( y2  y1 )
2
10  (2  8) 2  (11  y ) 2
10  (6)  (11  y )
2
10  36  (11  y )
2
100  36  (11  y)
2
2
2
64  (11  y)
2
8  11  y
8  11  y
3 y
8  11  y
19  y
10
CD = 17. If C is located at ( 3 ,1) and D is
located at ( x , 16 ), what are the possible
values of x ?
EF = 15. If E is located at ( -3 ,14) and F is
located at ( 6 , y ), which of the following is
a possible value of y ?
a) -26
b) 14
c) 2
d) -10
11
Pythagorean Theorem
leg
leg
A
c
B
b
a
C
12