1. 1.3 Segments and Their Measures
Unit 1 Day 2

2. Do Now Evaluate each expression. |4 – 7| |4.3 – 1.2| √(4 + 32)
√((-2)2 + 32) 3
3.1 5
√13

3. Using Segment Postulates
In geometry, rules that are accepted without proof are called ___________, or axioms.
Rules that are proved are called ___________.

4. Ex. 1: Finding the Distance Between Two Points
Measure the length of the segment to the nearest millimeter.
Use a metric ruler. Align one mark of the ruler with A. Then estimate the coordinate of B. For example if you align A with 3, B appears to align with 5.5.
AB = |5.5 – 3| = |2.5| = 2.5
The distance between A and B is about 2.5 cm.

5. 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.

6. 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?
= 170 mi.

7. 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

8. 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?
Yes, since PQ + QR = PR, P must be between P and R, by the segment addition postulate

9. 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 = _________________.
√[(x2 – x1)2 + (y2 – y1)2]
Relates to Pythagorean Theorem

10. Ex. 3 Using the Distance Formula
Find the length of the segments. AB AC AD
AB = √13
AC = √17
AD = √13

11. Congruence
Segments that have the same length are call _____________ segments.
Lengths are equal: AB ___ AD
Segments are congruent: ĀB __ ĀD
Congruent = ≅

12. 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.
Find the walking (taxicab) distance between A and B.
What would the (Euclidean) distance be if a diagonal street existed between A and B?
a. To walk from A to B, you would have to walk five blocks east and three blocks north.
5 * 340 = 1700 ft.
3 * 480 = 1440 ft.
Total: = 3140 ft.
b. Using the distance formula, AB = √4,963,600 ≈ 2228 ft.
(912 ft. less than walking distance)

13. 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
You cannot use the segment addition postulate because D, E, and F are not collinear. Therefore DF is not 5 cm. long. F
2 cm.