Transcript 1.3 Segments and Their Measures

1.3 Segments and Their
Measures
UNIT 1 DAY 2
Do Now
 Evaluate each expression.
1.
|4 – 7|
2.
|4.3 – 1.2|
3.
√(4 + 32)
4.
√((-2)2 + 32)
Using Segment Postulates
 In geometry, rules that are accepted without proof
are called ___________, or axioms.
 Rules that are proved are called ___________.
Ex. 1: Finding the Distance Between Two
Points
 Measure the length of the segment to the nearest
millimeter.
Postulate 1: Ruler Postulate
 A line segment can lined
up with coordinates on a
number line (like a ruler).
 The distance between
points A and B is the
absolute value of the
difference between the
coordinates of A and B.

AB is also called the length
of segment AB.
Ex. 2: Finding Distances on a Map
 Suppose the cities of Athens, Macon, and Albany,
GA, lie in a line. If it is 80 miles from Athens to
Macon and 90 miles from Macon to Albany, what is
the distance from Athens to Albany?
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.
 (Recall: When we say a
point is between two
other points, it implies
that the three points are
______________.)
 Also works for more than
two segments, as long as
all points collinear
Ex. 2A: Segment Addition Postulate
 Suppose PQ = 4.2 in., QR = 7.5 in., and PR = 11.7 in.
Is Q between P and R? How do you know?
Distance Formula
 The distance formula is used for computing the
distance between two points in a coordinate plane.

If A is (x1, y1) and B is (x2, y2), then the distance between A and
B is AB = _________________.
Ex. 3 Using the Distance Formula
 Find the length of the segments.

AB

AC

AD
Congruence
 Segments that have the same length are call
_____________ segments.

Lengths are equal: AB ___ AD

Segments are congruent: ĀB __ ĀD
Ex. 4: Finding Distance on a City Map
 On the map, the city blocks are each 340 feet apart
east-west and 480 feet apart north-south.
a)
Find the walking (taxicab)
distance between A and B.
b)
What would the (Euclidean)
distance be if a diagonal street
existed between A and B?
Closure
 In the diagram below, could you use the segment
addition postulate to find the distance from D to F?
Explain why or why not.
D
3 cm.
E
F
2 cm.