Measuring Segments

1
Measuring Segments
Chapter 1-4
Unit 1
For three collinear points A, B, and C, point B
is between A and C if AB BC AC.
Definition of Between
The measure of a segment is the distance
between the endpoints and is written as AB.
Measure of a segment
BC
AB
C
B
A
2
Measuring Segments
Chapter 1-4
Unit 1
The points on any line can be paired with real
numbers so that, given any two points P and Q on
the line, P corresponds to zero, and Q
corresponds to a positive number.
Ruler Postulate
The distance of any segment can be measured using
real numbers.
Segment Addition Postulate
If Q is between P and R, then PQ QR PR. If PQ
QR PR, then Q is between P and R.
3
Measuring Segments
Chapter 1-4
Unit 1
In a right triangle, the sum of the squares of
the measures of the legs is equal to the square
of the measure of the hypotenuse.
Pythagorean Theorem
c
a
b
4
Measuring Segments
Chapter 1-4
Unit 1
Find the distance between points H(2, 3) and
K(-3, -1) by using the Pythagorean Theorem.
Example 1
(2, 3)
4 units
c
(-3, -1)
5 units
5
Measuring Segments
Chapter 1-4
Unit 1
The distance d between any two points with
coordinates and is given by the
formula
Distance Formula
Congruent
To segments are congruent if they have the same
measure.
6
Measuring Segments
Chapter 1-4
Unit 1
Find JK for J(9, -5) and K(-6, 12).
Example 2